1. (a) The life time of a certain brand of bulbs produced by a company is normally distributed, with mean 210 hours and standard deviation 56 hours. What is the probability that a bulb picked at random from this company’s products will have a life time of:
(i) at least 300 hours,
(ii) at most 100 hours,
(iii) between 150 and 250 hours.
(b) In a contest, two friends, Kofi and Mensah were asked to solve a problem. The
probability that Kofi will solve it correctly is ' and the probability that Mensah
(
will solve it correctly is ) . Find the probability that neither of them solved it correctly.
*
Answers
Answer:
1a) (i) 0.0537
(ii) 0.0250
(iii) 0.6188
1b) The probability that neither Kofi nor Mensah solves the problem correctly = (9/20) = 0.45
Step-by-step explanation:
The complete Question is presented in the attached image to this answer.
1a) This is a normal distribution problem with
Mean lifetime of bulbs = μ = 210 hours
Standard deviation = σ = 56 hours
(i) at least 300 hours, P(x ≥ 300)
We first standardize 300 hours
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (300 - 210)/56 = 1.61
To determine the required probability
P(x ≥ 300) = P(z ≥ 1.61)
We'll use data from the normal probability table for these probabilities
P(x ≥ 300) = P(z ≥ 1.61) = 1 - P(z < 1.61)
= 1 - 0.94630 = 0.0537
(ii) at most 100 hours, P(x ≤ 100)
We first standardize 100 hours
z = (x - μ)/σ = (100 - 210)/56 = -1.96
To determine the required probability
P(x ≤ 100) = P(z ≤ -1.96)
We'll use data from the normal probability table for these probabilities
P(x ≤ 100) = P(z ≤ -1.96) = 0.0250
(iii) between 150 and 250 hours.
P(150 < x < 250)
We first standardize 150 and 250 hours
For 150 hours
z = (x - μ)/σ = (150 - 210)/56 = -1.07
For 250 hours
z = (x - μ)/σ = (250 - 210)/56 = 0.71
To determined the required probability
P(150 < x < 250) = P(-1.07 < z < 0.71)
We'll use data from the normal probability table for these probabilities
P(150 < x < 250) = P(-1.07 < z < 0.71)
= P(z < 0.71) - P(z < -1.07)
= 0.76115 - 0.14231
= 0.61884 = 0.6188 to 4 d.p.
1b) Probability that Kofi solves the problem correctly = P(K) = (1/4)
Probability that Mensah solves the problem correctly = P(M) = (2/5)
Probability that Kofi does NOT solve the problem correctly = P(K') = 1 - P(K) = 1 - (1/4) = (3/4)
Probability that Mensah does NOT solve the problem correctly = P(M') = 1 - P(M) = 1 - (2/5) = (3/5)
To find the probability that neither of them solves the problem correctly, we first make the logical assumption that the probabilities of either of them solving the problem are independent of each other.
Hence, the probability that neither of them solves the problem correctly = P(K' n M')
P(K' n M') = P(K') × P(M') = (3/4) × (3/5) = (9/20) = 0.45
Hope this Helps!!!
Related Questions
Manuel is 6 years older than melissa. In 6 years the sum of their ages will be 52. How old is manuel now?
_______years old
Answers
Answer:
58
Step-by-step explanation:
Answer:
58
Step-by-step explanation:
lolololololololol
There are about 208,000,000,000 different 8-letter passwords that can be formed using a 26-letter
alphabet.
Express this number using scientific notation.
0 2.08 x 1011
O 208 10
O 20.8 x 1010
0 0.208 x 1012
Answers
Answer:
2.08 x 10^11
Step-by-step explanation:
To put a number into scientific notation you move the decimal to the spot right after the first digit. To figure out what the power is you count how many digits you moved it past in order to get to the spot you want it (right after the first digit; in this case the 2)
So in this case you would move the decimal from the end of the number backwards past 9 zeros, the 8, and another zero, which is a total of 11 digits.
From there you take the number with the new decimal place and multiply by 10 to the power of the number you counted earlier, which for this example is 11
So the final answer is 2.08 x 10^11
How many solutions are there to the equation below?
5(x + 10) - 25 = 5x + 25
O A. 1
OB.O
O C. Infinitely many
Answers
Answer: Infintely many
Step-by-step explanation:
5(x + 10) - 25 = 5x + 25
5x +50 - 25 = 5x + 25
5x +25 = 5x + 25
Same equation
What is the mean of the following set of data?
{6,9,3, 8, 9,3,4}
Answers
Answer:
6
Step-by-step explanation:
Add all the numbers together and divide by the amount of numbers
6+9+3+8+9+3+4= 42
42/7 = 6
Answer:
6
Step-by-step explanation:
To find the mean or the average of the data set, you add all the numbers together and then divide the sum by the number of numbers in the data set.
6+9+3+8+9+3+4 =42
Then divided by the # of terms.
42/7= 6
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5), as instructed, to ?nd a second solution y2(x)
y"+2y'+y=0; y1=xe^-x.
Answers
Answer:
[/tex]y2=e^(-x)[/tex]
Step-by-step explanation:
CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLANATION
The points J(-1,-9) and K(5,1) are endpoints of a diameter of circle S. Which equation represents circle S? A. (x − 2)2 + (y + 4)2 = 34 B. (x − 2)2 + (y + 4)2 = 136 C. (x + 2)2 + (y − 4)2 = 34 D. (x + 2)2 + (y − 4)2 = 136
Answers
Answer:
the equation of the circle is
[tex](x-2)^2+(y+4)^2 = 34[/tex]
Step-by-step explanation:
Recall that the equation of a circle is given by [tex](x-h)^2+(y-k)^2 = r^2[/tex] where r is the radius, and (h,k) is the center. Recall that given two points that are the endpoints of a diameter, the center of the circle is their correspondent midpoint. Also, recall that given points (a,b), (c,d) their midpoint is obtained by [tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]
In this case we are given the endpoints (-1,-9), (5,1). So the center of the circle is the midpoint obtained by [tex](\frac{-1+5}{2},\frac{-9+1}{2}) = (2, -4)[/tex]. Recall that the radius of a circle is the distance from the radius to any of the points of the circle. So, the radius is the distance between the center and the point (-1,-9). We will calculate r^2, by using the distance formula. REcall that the distance between points (a,b), (c,d) is given by
[tex]\sqrt[]{(a-c)^2+(b-d)^2}[/tex]. So, its square is
[tex](a-c)^2+(b-d)^2[/tex].
In our case,
[tex]r^2 = (2-(-1))^2+(-4-(-9))^2 = 3^2+5^2 = 34[/tex]
So, the equation of the circle is
[tex](x-2)^2+(y+4)^2 = 34[/tex]
pls halp me TwT im l
confused since quarantine happened reee
lateral area
surface area
volume
Answers
Answer:
22 is the answer but which country are you from
Answer:
22
Step-by-step explanation:
Write a quadratic function f whose only zero is −10.
Answers
function is: f(x)=(x+10)^2
The quadratic function f whose only zero is −10 should be [tex]f(x)=(x+10)^2[/tex].
What is a quadratic function?A quadratic function should be the one of the form f(x) [tex]= ax^2 + bx + c[/tex], where a, b, and c are numbered with a not equal to zero. The graph of a quadratic function is a curve known a parabola.
So here we assume that the The quadratic function f whose only zero is −10 should be [tex]f(x)=(x+10)^2[/tex].
Learn more about function here: https://brainly.com/question/13223520
A stereo store is offering a special price on a complete set ofcomponents (receiver, compact disc player, speakers, cassette deck)ie one of each. A purchaser is offered a choice ofmanufacturer for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood
CD Player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Cassette Deck: Onkyo, Sony, Teac, Technics
A switch board display in the store allows a customer to hooktogether any selection of components (consisting of one of eachtype). Use the product rules to answer the following questions.
a. In how many ways can one component of each type beselected?
b. In how many ways can components be selected if boththe receiver and the cd player are to be sony?
c. In how many ways can components be selected if noneis to be sony?
d. In how many ways can a selection be made if at leastone sony component is to be included?
e. If someone flips the switches on the selection in acompletely random fashion, what is the probability that the systemselected contains at least one sony component? Exactly onesony component?
Answers
Answer:
Step-by-step explanation:
(a)
The number of receivers is 5.
The number of CD players is 4.
The number of speakers is 3.
The number of cassettes is 4.
Select one receiver out of 5 receivers in [tex]5C_1[/tex] ways.
Select one CD player out of 4 CD players in [tex]4C_1[/tex] ways.
Select one speaker out of 3 speakers in [tex]3C_1[/tex] ways.
Select one cassette out of 4 cassettes in [tex]4C_1[/tex] ways.
Find the number of ways can one component of each type be selected.
By the multiplication rule, the number of possible ways can one component of each type be selected is,
The number of ways can one component of each type be selected is
[tex]=5C_1*4C_1*3C_1*4C_1\\\\=5*4*3*4\\\\=240[/tex]
Part a
Therefore, the number of possible ways can one component of each type be selected is 240.
(b)
The number of Sony receivers is 1.
The number of Sony CD players is 1.
The number of speakers is 3.
The number of cassettes is 4.
Select one Sony receiver out of 1 Sony receivers in ways.
Select one Sony CD player out of 1 Sony CD players in ways.
Select one speaker out of 3 speakers in ways.
Select one cassette out of 4 cassettes in [tex]4C_1[/tex] ways.
Find the number of ways can components be selected if both the receiver and the CD player are to be Sony.
By the multiplication rule, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is,
Number of ways can one components of each type be selected
[tex]=1C_1*1C_1*3C_1*4C_1\\\\=1*1*3*4\\\\=12[/tex]
Therefore, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is 12.
(c)
The number of receivers without Sony is 4.
The number of CD players without Sony is 3.
The number of speakers without Sony is 3.
The number of cassettes without Sony is 3.
Select one receiver out of 4 receivers in 4C_1 ways.
Select one CD player out of 3 CD players in 3C_1 ways.
Select one speaker out of 3 speakers in 3C_1 ways.
Select one cassette out of 3 cassettes in 3C_1 ways.
Find the number of ways can components be selected if none is to be Sony.
By the multiplication rule, the number of ways can components be selected if none is to be Sony is,
[tex]=4C_1*3C_1*3C_1*3C_1\\\\=108[/tex]
[excluding sony from each of the component]
Therefore, the number of ways can components be selected if none is to be Sony is 108.
(d)
The number of ways can a selection be made if at least one Sony component is to be included is,
= Total possible selections -Total possible selections without Sony
= 240-108
= 132
Therefore, the number of ways can a selection be made if at least one Sony component is to be included is 132.
(e)
If someone flips the switches on the selection in a completely random fashion, the probability that the system selected contains at least one Sony component is,
[tex]= \text {Total possible selections with at least one Sony} /\text {Total possible selections}[/tex]
= 132 / 240
= 0.55
The probability that the system selected contains exactly one Sony component is,
[tex]= \text {Total possible selections with exactly one Sony} /\text {Total possible selections}[/tex][tex]\frac{1C_1*3C_1*3C_1*3C_1+4C_11C_13C_13C_1+4C_13C_13C_13C_1}{240} \\\\=\frac{99}{240} \\\\=0.4125[/tex]
Therefore, if someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains at least one Sony component is 0.55.
If someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains exactly one Sony component is 0.4125.
A newly proposed endoscopy method used to screen for colon cancer is tested among a random sample of the population. Given that 16 individuals from a test population of 100,000 individuals has colon cancer and 14 individuals test positive for colon cancer, the researchers should determine the sensitivity of the newly proposed screening method is .875.
a. True
b. False
Answers
Answer: True
Step-by-step explanation:
Sensitivity in such a scenario is used to measure the accuracy of the screening method. In other words, how effective is the screening method at detecting Colon Cancer.
The sensitivity of the method can be calculated by dividing the amount of people that it showed as positive by the number of people that were actually tested.
The number of people who showed positive were 14 and the amount of people tested were 16.
Sensitivity therefore is,
= 14/16
= 0.875
They should indeed determine the sensitivity of the newly proposed screening method to be .875.
(Old Final Exam Problem-A2011) A right circular cone of height h and base radius r has total surface area S consisting of its base area plus its side area, leading to the formula: S= π r2 + π r r2+h2 Suppose you start out with a cone of height 8 cm and base radius 6 cm, and you want to change the dimensions in such a way that the total surface area remains the same. Suppose you increase the height by 15/100. In this problem, use tangent line approximation to estimate the new value of r so that the new cone has the same total surface area. The estimated value of r =
Answers
Answer:
5.972 cm
Step-by-step explanation:
Using implicit differentiation, we have ...
0 = (2πr +π(√(r^2+h^2) +r^2/√(r^2+h^2))·dr/dh +πrh/√(r^2+h^2)
For the given values of r and h, this is ...
0 = (12π +π(10 +36/10))dr/dh +48π/10
dr/dh = -4.8/(12+13.6) = -0.1875
Then the tangent line is ...
r = -0.1875(h -8) +6
__
For a height of 8 +15/100 = 8.15, the estimated value of r is ...
r = -0.1875(8.15 -8) +6 = -0.1875(0.15) +6 = 5.971875
The estimated value of r is 5.972 cm.
simplify the expression 2\3(-4)-(1/6-8/6
Answers
Answer:
1/8
Step-by-step explanation:
Answer:
When you simplify it, you get the answer of 1.
Step-by-step explanation:
Order of operation rules are required that you multiply and divide before you carrying out addition and/or subtraction.
So, simplify 2/3 / (-4) first, obtaining -1/6.
Now, you have -1/6 - 1/6 + 8/6, which combines to 1 or 6/6.
Can someone help me with the answer
Answers
Answer:
D. 129°
Step-by-step explanation:
Angles XZY and XZV form a linear pair, so are supplementary.
angle XZV = 180° -51° = 129°
f(x) = (x - 5)(5x + 2)
lesser x =
greater x =
Answers
Answer:
hope
this
is
correct
Plz help fast Jack, John, Lily, and Sara want to take a picture together. In how many ways can they are arranged?
Answers
Answer:
The best estimate would be around 10-16
Step-by-step explanation:
The think is that they can be in many orders and since there is four of them it would be more orders.
Hope this helps
One study revealed that a child under the age of 10 watches television 4.5 hours per day. A group of families from a certain comunity would like to beleive that their children watch television less than the national average. A random sample of 14 children from the community yielded a mean of 4.1 hours per day with standard deviation of 1.2. Test the appropriate hypothesis at the level of significance 0.01. Assume the viewing time is normally distributed and interpret your results.
Answers
Answer:
[tex]t=\frac{4.1-4.5}{\frac{1.2}{\sqrt{14}}}=-1.25[/tex]
The degrees of freedom are given by:
[tex] df=n-1= 14-1=13[/tex]
And the p value would be:
[tex]p_v =P(t_{13}<-1.25)=0.117[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 4.5 minutes.
Step-by-step explanation:
Information given
[tex]\bar X=4.1[/tex] represent the sample mean
[tex]s=1.2[/tex] represent the sample deviation
[tex]n=14[/tex] sample size
[tex]\mu_o =4.5[/tex] represent the value to test
[tex]\alpha=0.01[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is less than 4.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 4.5[/tex]
Alternative hypothesis:[tex]\mu < 4.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{4.1-4.5}{\frac{1.2}{\sqrt{14}}}=-1.25[/tex]
The degrees of freedom are given by:
[tex] df=n-1= 14-1=13[/tex]
And the p value would be:
[tex]p_v =P(t_{13}<-1.25)=0.117[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 4.5 minutes.
the sum of a number and 9 is -7. What does that mean or what's the equation
Answers
Answer: x+9= -7
Step-by-step explanation:
What this statement means is that the sum or combining/adding of 9 and another number gives you -7 as the answer. We can write an equation to figure out what the other number is.
Let's use x as the unknown/other number.
x+9= -7
That is what your set up equation would look like. To solve for x, you simply subtract 9 on both sides.
x=-16
I need 6th question in the paper
Answers
Answer:
8
Step-by-step explanation:
[tex] a = 1 - \sqrt{2} [/tex]
[tex] (a - \dfrac{1}{a})^3 = [/tex]
[tex] = (\dfrac{a^2}{a} - \dfrac{1}{a})^3 [/tex]
[tex] = (\dfrac{a^2 - 1}{a})^3 [/tex]
[tex] = (\dfrac{(a + 1)(a - 1)}{a})^3 [/tex]
[tex] = (\dfrac{(1 - \sqrt{2} + 1)(1 - \sqrt{2} - 1)}{a})^3 [/tex]
[tex]= (\dfrac{(2 - \sqrt{2})(-\sqrt{2})}{1 - \sqrt{2}})^3[/tex]
[tex]= (\dfrac{(-2\sqrt{2} + \sqrt{2}\sqrt{2}}{1 - \sqrt{2}})^3[/tex]
[tex]= (\dfrac{2 - 2\sqrt{2}}{1 - \sqrt{2}})^3[/tex]
[tex]= (\dfrac{2(1 - \sqrt{2})}{1 - \sqrt{2}})^3[/tex]
[tex] = 2^3 [/tex]
[tex] = 8 [/tex]
A survey said that 3 out of 5 students enrolled in higher education took at least one online course last fall. Explain your calculations and reasoning for the following: a) If you were to pick at random 1 student enrolled in higher education, what is the probability that student took at least one online course? b) If you were to pick at random 1 student enrolled in higher education, what is the probability that student did not take an online course? c) Now, consider the scenario that you are going to select random select 4 students enrolled in higher education. Find the probability that All 4 students selected took online courses
Answers
Answer:
a) 60% probability that student took at least one online course
b) 40% probability that student did not take an online course
c) 12.96% probability that all 4 students selected took online courses.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they took at least one online course last fall, or they did not. The probability of a student taking an online course is independent of other students. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
3 out of 5 students enrolled in higher education took at least one online course last fall.
This means that [tex]p = \frac{3}{5} = 0.6[/tex]
a) If you were to pick at random 1 student enrolled in higher education, what is the probability that student took at least one online course?
This is P(X = 1) when n = 1. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{1,1}.(0.6)^{1}.(0.4)^{0} = 0.6[/tex]
60% probability that student took at least one online course.
b) If you were to pick at random 1 student enrolled in higher education, what is the probability that student did not take an online course?
This is P(X = 0) when n = 1.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{1,1}.(0.6)^{0}.(0.4)^{1} = 0.4[/tex]
40% probability that student did not take an online course
c) Now, consider the scenario that you are going to select random select 4 students enrolled in higher education. Find the probability that all 4 students selected took online courses
This is P(X = 4) when n = 4.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.6)^{4}.(0.4)^{0} = 0.1296[/tex]
12.96% probability that all 4 students selected took online courses.
The area of the triangle below is 2/5 square foot. What is the length, in feet, of the base of the triangle? Area = bh/2
Answers
Answer:
2/3 feet.
Step-by-step explanation:
We have to calculate the length of the base of the triangle, in this case they give us the area of the triangle but still it is necessary to know the height of the triangle to calculate the length of the base, otherwise it would be impossible.
I have found an image where the graph is, which I will attach where you can see that the height is 6/5 ft. The area of the triangle is:
A = b * h / 2
solved for b which is the length of the base of the triangle would be:
b = 2 * A / h
replacing:
b = 2 * (2/5) / (6/5)
b = 20/30
b = 2/3
Which means that the length of the base of that triangle is 2/3 feet.
AnswerSo C:
Step-by-step explanation:
How would I find the domain and range of this graph?
Answers
Answer:
Domain: [-3, 5]
Range: [-5, 4]
Step-by-step explanation:
The first thing is to define what is the domain and the range. The domain of a function f (x) is the set of all the values for which the function is defined, and the range of the function is the set of all the values that f takes.
In other words, the domain is the value on the "x" axis and the range is the value on the "y" axis.
In this case, both are an interval, the domain would be from -3 to 5 and in the case of the range it would be from -5 to 4.
Domain: [-3, 5]
Range: [-5, 4]
Given f(x) = 6x + 2, find f(x-3)
Answers
Answer:
6x -16
Step-by-step explanation:
f(x) = 6x + 2
f(x-3) =
Replace x with x-3
f(x) = 6(x-3) + 2
Distribute
= 6x - 18 +2
= 6x -16
The right answer is 6x-16
please see the attached picture for full solution
Hope it helps
Good luck on your assignment..
a bus drives at 66 km at an average speed of 66 km/h. how long does the journey take?
Answers
Answer:
1 hour
Step-by-step explanation:
From Distance = speed × time
time = Distance/ speed
=66/66 = 1 hour
A sample of size =n72 is drawn from a population whose standard deviation is =σ25. Part 1 of 2 (a) Find the margin of error for a 95% confidence interval for μ. Round the answer to at least three decimal places. The margin of error for a 95% confidence interval for μ is . Part 2 of 2 (b) If the sample size were =n89, would the margin of error be larger or smaller?
Answers
Answer:
a) margin of error ME = 5.77
b) Margin of error becomes smaller
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
x+/-ME
Where margin of error ME = zr/√n
a)
Given that;
Mean = x
Standard deviation r = 25
Number of samples n = 72
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
ME = 1.96(25/√72)
ME = 1.96(2.946278254943)
ME = 5.774705379690
ME = 5.77
b)
For n = 89
ME = 1.96(25/√89)
ME = 1.96(2.649994700015)
ME = 5.193989612031
ME = 5.19
5.19 is smaller than 5.77 in a) above. So,
Margin of error becomes smaller
Simplify
sin^2x+tan^2x+cos^2x
Answers
Answer:
sec²x
Step-by-step explanation:
sin²x + tan²x + cos²x
sin²x + cos²x + tan²x
1 + tan²x ( sin²x + cos²x = 1 )
sec²x ( 1 + tan²x = sec²x )
Answer:
Step-by-step explanation:
SIN^2x + tan^2 x + cos^2x
= x( sin^2 + tan^2+cos^2)
=x(1+tan^2) since sin^2+cos^2 =1
=xsec^2 ( since sec^2 = 1+tan^2)
=sec^2x
hope it helps
In the game of roulette, a player can place a $4 bet on the number 10 and have a 1/38 probability of winning. If the metal ball lands on 10, the player gets to keep the $4 paid to play the game and the player is awarded an additional $140. Otherwise, the player is awarded nothing and the casino takes the player’s $4. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?
Answers
this one is kinda Hard ill do sum research and help
Flow meters are installed in urban sewer systems to measure the flows through the pipes. In dry weatherconditions (no rain) the flows are generated by waste-water from households and industries, together withsome possible drainage from water stored in the topsoil from previous rainfalls. In a study of an urbansewer system, the following values were obtained for flowrates during dry weather conditions:
423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0
Assume that the flow rates are normally distributed.
a. Construct a 98% two-sided confidence interval for the standard deviation of the flow rate under dry weather conditions.
b. Explain, only using words, the meaning of the CI you determined in (a).
Answers
Answer:
a) [tex]\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}[/tex]
[tex] 363.90 \leq \sigma^2 \leq 4430.80[/tex]
Now we just take square root on both sides of the interval and we got:
[tex] 19.08 \leq \sigma \leq 66.56[/tex]
b) For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56
Step-by-step explanation:
423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0
Part a
The confidence interval for the population variance is given by the following formula:
[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]
On this case we need to find the sample standard deviation with the following formula:
[tex]s=sqrt{\frac{\sum_{i=1}^8 (x_i -\bar x)^2}{n-1}}
And in order to find the sample mean we just need to use this formula:
[tex]\bar x =\frac{\sum_{i=1}^n x_i}{n}[/tex]
The sample deviation for this case is s=30.23
The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:
[tex]df=n-1=9-1=8[/tex]
The Confidence interval is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and the critical values are:
[tex]\chi^2_{\alpha/2}=20.09[/tex]
[tex]\chi^2_{1- \alpha/2}=1.65[/tex]
And replacing into the formula for the interval we got:
[tex]\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}[/tex]
[tex] 363.90 \leq \sigma^2 \leq 4430.80[/tex]
Now we just take square root on both sides of the interval and we got:
[tex] 19.08 \leq \sigma \leq 66.56[/tex]
Part b
For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56
Solve x-6y=17 for y, please help
Answers
Answer:
y = x/6 - 17/6
Step-by-step explanation:
x - 6y = 17
<=>6y = x - 17
<=> y =x/6 - 17/6
Hope this helps!
The graph below represents a recent 10 meter race between two remote control cars.
10 I'm
Remote Control Car Race
Answers
Answer:
It's B I think.
Step-by-step explanation: If they the lines intersected then it'd mean they crashed.
The graph below shows a recent 10-meter race between two remote-control automobiles. The racial assertions in A, B, and C are true.
What is a graph?A graph that shows the relationship between two or more variables, each of which is measured along one of two axes that are at right angles to one another.
At 6 meters into the race, the blue car overtook the red car because, at that moment, the blue car had a bigger distance than the red car.
Due to the greater slope of the blue vehicle's path compared to the red car's line, the blue car is faster.
Because the blue car's x-intercept is at (3, 0), where x stands for time and y for distance from the starting line, it began 3 seconds later than the other cars.
Hence Statements B, C, and D about race are true.
Q.The graph below represents a recent 10-meter race between two remote control cars.
A graph titled Remote Control Car Race has seconds after the race starts on the x-axis and distance from the start line (meters) on the y-axis. A line labeled red car goes through (3, 2) and (6, 4). A line labeled blue car goes through (3, 0) and (5, 2).
Which statements about race are true? Check all that apply.
The red car won the race because it started above the blue car.
The cars crashed 9 seconds into the race because that is the point of intersection, and neither car continued on after that point in time.
The blue car passed the red car at 6 m into the race because that is the point of intersection, and the blue car has a greater distance than the red car after that time.
The blue car is faster because the slope of its line is steeper than the slope of the line representing the red car.
The blue car started 3 seconds late because it has an x-intercept of (3, 0) and x represents the time and y represents the distance from the starting line.
learn more about graphs here :
https://brainly.com/question/10712002
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The yellow boxes on the bottom are the answers. Please help TYSM
Answers
Answer:
[tex]1.\ 8p = 64, p =8[/tex]
[tex]2. -\dfrac{w}{4} = 8, w = -32[/tex]
[tex]3. -5c = -20, c =4[/tex]
[tex]4.\ 9m=45, m = 5[/tex]
[tex]5. \dfrac{b}{25} = -3, b =-75[/tex]
[tex]6. \dfrac{d}{-2} = 20, d=-40[/tex]
Step-by-step explanation:
Now let us see the detailed solution of each part:
Part 1:
[tex]8p -15 = 49\\\Rightarrow 8p =49+15\\\Rightarrow 8p = 64\\\Rightarrow p =8[/tex]
Part 2:
[tex]\dfrac{-w}{4}+18=26\\\Rightarrow \dfrac{-w}{4} = 26-18\\\Rightarrow \dfrac{-w}{4} = 8\\\Rightarrow -w = 8 \times 4\\\Rightarrow w =-32[/tex]
Part 3:
[tex]-5c-15=-35\\\Rightarrow -5c = -35 +15\\\Rightarrow -5c = -20\\\Rightarrow c = 4[/tex]
Part 4:
[tex]9m +10=55\\\Rightarrow 9m =55-10\\\Rightarrow 9m =45\\\Rightarrow m =5[/tex]
Part 5:
[tex]\dfrac{b}{25}-83=-86\\\Rightarrow \dfrac{b}{25} = -86 +83\\\Rightarrow \dfrac{b}{25} = -3\\\Rightarrow b = -75[/tex]
Part 6:
[tex]\dfrac{d}{-2}+85=105\\\Rightarrow \dfrac{d}{-2} = 105-85\\\Rightarrow \dfrac{d}{-2} = 20\\\Rightarrow d=20 \times -2\\\Rightarrow d =-40[/tex]
Please refer to attached image for the answers.