Answer:
60.85% probability that the sample mean is between $1.4 million and $1.5 million per year
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
In millions of dollars.
[tex]\mu = 1.47, \sigma = 0.3, n = 30, s = \frac{0.3}{\sqrt{30}} = 0.0548[/tex]
What is the probability that the sample mean is between $1.4 million and $1.5 million per year?
This is the pvalue of Z when X = 1.5 subtracted by the pvalue of Z when X = 1.4. So
X = 1.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.5 - 1.47}{0.0548}[/tex]
[tex]Z = 0.55[/tex]
[tex]Z = 0.55[/tex] has a pvalue of 0.7088
X = 1.4
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.4 - 1.47}{0.0548}[/tex]
[tex]Z = -1.28[/tex]
[tex]Z = -1.28[/tex] has a pvalue of 0.1003
0.7088 - 0.1003 = 0.6085
60.85% probability that the sample mean is between $1.4 million and $1.5 million per year
Answer:
[tex] z= \frac{1.4-1.47}{\frac{0.3}{\sqrt{30}}}= -1.278[/tex]
[tex] z= \frac{1.5-1.47}{\frac{0.3}{\sqrt{30}}}= 0.548[/tex]
And we can find the probability with this difference:
[tex] P(-1.278<z<0.548) = P(z<0.548) -P(z<-1.278) =0.708-0.101= 0.607[/tex]
So then the probability that the sample mean is between $1.4 million and $1.5 million per year is 0.607
Step-by-step explanation:
For this case we have the following info given:
[tex] \mu = 1.47[/tex] the true mean for the problem
n =30 represent the sample size
[tex] \sigma = 0.3 millions[/tex] represent the population deviation
And we want to find this probability
[tex] P(1.4< \bar X <1.5)[/tex]
And we can use the z score given by:
[tex] z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z scores for the limits we got:
[tex] z= \frac{1.4-1.47}{\frac{0.3}{\sqrt{30}}}= -1.278[/tex]
[tex] z= \frac{1.5-1.47}{\frac{0.3}{\sqrt{30}}}= 0.548[/tex]
And we can find the probability with this difference:
[tex] P(-1.278<z<0.548) = P(z<0.548) -P(z<-1.278) =0.708-0.101= 0.607[/tex]
So then the probability that the sample mean is between $1.4 million and $1.5 million per year is 0.607
Champagne is best when the bubbles are concentrated in the wine. A group of scientists compared gentle and splashing pouring methods for champagne by measuring the amount of bubbles in each glass of champagne poured two different ways at three different temperatures. The following data present the pattern of results obtained in the study.
Chane of temperature
40 46 52
Gentle pour n=10 n=10 n=10
M=7 M=3 M=2
SS=64 SS=57 SS=47
Splashing pour n=10 n=10 n=10
M=5 M=1 M=0
SS=56 SS=54 SS=46
Required:
a. Use a two-factor ANOVA with α= 0.05 to evaluate the mean differences.
b. Briefly explain how temperature and pouring influence the bubbles in champagne according to this pattern of results.
Answer:
??????
Step-by-step explanation:
4. Automobile policies are separated into two groups: low-risk and high-risk. Actuary Rahul examines low-risk policies, continuing until a policy with a claim is found and then stopping. Actuary Toby follows the same procedure with high-risk policies. Each low-risk policy has a 10% probability of having a claim. Each high-risk policy has a 20% probability of having a claim. The claim statuses of polices are mutually independent. Calculate the probability that Actuary Rahul examines fewer policies than Actuary Toby.
Answer:
Step-by-step explanation:
for n ∈ N
Since Actuary Rahul examines low-risk policies, continuing until a policy with a claim is found and then stopping.
∴ the probability that Actuary Rahul examines exactly n policies
[tex](0.9)^{n-1}.(0.1)---(1)[/tex]
the probability that Actuary Toby examines more than exactly n policies
[tex](0.8)^n---(2)[/tex]
Given that policies are actually independent
∴ the probability that the event (1) and (2) happens simultaneously is
[tex](0.9)^{n-1}*(0.1)*(0.8)^n[/tex]
∴ the probability that Actuary Rahul examines fewer policies than Actuary Toby
[tex]\sum ^\infty _{n=1} (0.9)^{n-1}*(0.1)*(0.8)^n\\\\=(\frac{0.1}{0.9} \sum ^\infty _{n=1}(0.72)^n\\\\=\frac{1}{9} (\frac{0.72}{0.28} )\\\\=\frac{2}{7} \\\\=0.2857[/tex]
the probability that Actuary Rahul examines fewer policies than Actuary Toby is 0.2857HELP PLEASE WILL MARK AS BRAINLIST
Answer:
If x + 5x = 90, 6x = 90 so x = 15, 5x = 75.
Answer: x= 15, 5x=75
Step-by-step explanation:
x=15
x+5x=90
Add similar elements
6x=90
6x/6=90/6
x=15
5x=75
x=15
5x=15x5
15x5=75
a/50 = 3/5 Solve for “a” by cross multiplying then divide.
Answer:
a = 30
Step-by-step explanation:
a/ 50 = 3/5
Using cross products
a*5 = 50 *3
5a = 150
Divide each side by 5
5a/5 = 150/5
a = 30
Answer:
[tex]a =30[/tex]
Step-by-step explanation:
[tex] \frac{a}{50} = \frac{3}{5} [/tex]
[tex]use \: \: \: cross \: \: multiple[/tex]
[tex]5a = 50 \times 3 \\ 5a = 150 \\ \frac{5a}{5} = \frac{150}{5} \\ a = 30[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Conner and Alexandra are 260 feet apart when they start walking toward one another. Alexandra walks twice as fast as Conner so whenever Conner travels x feet, Alexandra travels 2 x feet. Let x represent the number of feet Conner has traveled since he started walking toward Alexandra. Write an expression in terms of x to represent the total number of feet Conner and Alexandra have walked toward one another. 3x Correct Write an expression in terms of x to represent the distance (in feet) between Conner and Alexandra.
Answer:
i) 3x
ii) d = 260 - 3x
Step-by-step explanation:
Given:
Conner traveled x feet
Alexandra traveled 2x feet
Total distance = 260 ft
i) The expression in terms of x to represent the total number of feet Conner and Alexandra have walked toward one another will be:
This will be the total number of feet they have walked towards one another
= x + 2x
= 3x
ii) An expression in terms of x to represent the distance (in feet) between Conner and Alexandra.
This will be to find the distance between Conner and Alexandra.
Thus, distance between them will be:
d = 260 - (x + 2x)
d = 260 - 3x
Can someone please give me the answer to this?
Answer:
About 36.87
Step-by-step explanation:
The sine of an angle in a right triangle is the length of the opposite side divided by the length of a hypotenuse, which in this case is 3/5. Therefore, the measure of the angle is the arcsin of 3/5 or about 36.87 degrees. Hope this helps!
Which statement best describes the expression fraction 1 over 2 x (14 − 6) x 6 + 4?
Answer:
Find half the difference of 14 and 6, multiply by 6, then add 4.(B)
Step-by-step explanation:
WIll give brainliest !! PLEASE PLEASE !!
Answer:
a) y=4x-3
Step-by-step explanation:
Find the slope by comparing the values within one column. If you subtract 1 from -3, you'll get the value of 4. You then notice that each time, the value increases by 4. Since the y= column is increasing by one, the value therefore remains constant because 4 divided by 1 is always 4.
Now, to find the coefficient, just look at where the y value is 0. Whatever number x is when the value is 0, that will be your coefficient because it is the y-intercept (the initial starting value); in this case -3
Answer:
A
Step-by-step explanation:
First, calculate the slope by doing rise over run.
We can do this between the first 2 points:
[tex]\frac{4}{1}[/tex] = 4
The slope is positive 4, and the y-intercept is (0, -3)
The equation is A, y = 4x - 3
(1 point) Let P(t) be the performance level of someone learning a skill as a function of the training time t. The derivative dPdt represents the rate at which performance improves. If M is the maximum level of performance of which the learner is capable, then a model for learning is given by the differential equation dPdt=k(M−P(t)) where k is a positive constant. a) First solve this differential equation for P(t) using C as your final (simplified) constant parameter introduced by integrating.
Answer:
[tex]P(t)=M+Ce^{-kt}[/tex]
Step-by-step explanation:
Given the differential model
[tex]\dfrac{dP}{dt}=k[M-P(t)][/tex]
We are required to solve the equation for P(t).
[tex]\dfrac{dP}{dt}=kM-kP(t)\\$Add kP(t) to both sides\\\dfrac{dP}{dt}+kP(t)=kM\\$Taking the integrating factor\\e^{\int k dt} =e^{kt}\\$Multiply all through by the integrating factor\\\dfrac{dP}{dt}e^{kt}+kP(t)e^{kt}=kMe^{kt}\\\dfrac{dP}{dt}e^{kt}=kMe^{kt}\\(Pe^{kt})'=kMe^{kt} dt\\$Take the integral of both sides with respect to t\\\int (Pe^{kt})'=\int kMe^{kt} dt\\Pe^{kt}=kM \int e^{kt} dt\\Pe^{kt}=\dfrac{kM}{k} e^{kt} + C_0, C_0$ a constant of integration[/tex]
[tex]Pe^{kt}=Me^{kt} + C\\$Divide both side by e^{kt}\\P(t)=M+Ce^{-kt}\\P(t)=M+Ce^{-kt}\\$Therefore:\\P(t)=M+Ce^{-kt}[/tex]
The average amount of a beverage in randomly selected 16-ounce beverage can is 16.18 ounces with a standard deviation of 0.4 ounces. If a random sample of sixty-five 16-ounce beverage cans are selected, what is the probability that the mean of this sample is less than 16.1 ounces of beverage? Answer: (round to 4 decimal places)
Answer:
The probability that the mean of this sample is less than 16.1 ounces of beverage is 0.0537.
Step-by-step explanation:
We are given that the average amount of a beverage in randomly selected 16-ounce beverage can is 16.18 ounces with a standard deviation of 0.4 ounces.
A random sample of sixty-five 16-ounce beverage cans are selected
Let [tex]\bar X[/tex] = sample mean amount of a beverage
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean amount of a beverage = 16.18 ounces
[tex]\sigma[/tex] = standard deviation = 0.4 ounces
n = sample of 16-ounce beverage cans = 65
Now, the probability that the mean of this sample is less than 16.1 ounces of beverage is given by = P([tex]\bar X[/tex] < 16.1 ounces)
P([tex]\bar X[/tex] < 16.1 ounces) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{16.1-16.18}{\frac{0.4}{\sqrt{65} } }[/tex] ) = P(Z < -1.61) = 1 - P(Z [tex]\leq[/tex] 1.61)
= 1 - 0.9463 = 0.0537
The above probability is calculated by looking at the value of x = 1.61 in the z table which has an area of 0.9591.
what are the cubic units? Pleaseee
Answer: pls mark me brainiest
Step-by-step explanation:
I am very sure that the answer is V≈351.86
Answer:
112π
Step-by-step explanation:
Cubic units are units when talking in the 3rd dimension
The volume of a cylinder is πr² x h
find the area of the base first.
since we can write it in terms of π, don't worry about decimals.
The radius is 4.
plug it in, the base's area is 16π. Multiply that by the height, 7.
16(7)π
112π is the volume
The perimeter of the original rectangle on the left is 30 meters. The perimeter of the reduced rectangle on the right is 24 meters.
A small rectangle has a length of 8 meters. A larger rectangle has a width of x.
What is x, the width of the original rectangle on the left? Round to the nearest hundredth if necessary.
5 meters
8 meters
10 meters
12 meters
Answer:
5 meters
Step-by-step explanation:
If the smallest rectangle has a length of 8 meters, and a perimeter of 24 meters then its width is given by:
[tex]24 = 2*8+2*W_1\\W_1= 4\ meters[/tex]
We can conclude that the width is half of the length for both rectangles. Therefore, the width of the larger rectangle, with a perimeter of 30 meters, is:
[tex]30 = 2*W_2+2*L_2\\30 = 2*W_2+4*W_2\\W_2=5\ meters[/tex]
The width of the original rectangle is 5 meters.
Answer:
5
Step-by-step explanation:
Find the scale factor
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
Let
z -----> the scale factor
P1 -----> the perimeter of the reduced rectangle on the right
P2 ----> the perimeter of the original rectangle on the left
substitute
step 2
Find the width of the reduced rectangle on the right
substitute the given values.
Find the width of the original rectangle on the left.
To find the width of the original rectangle on the left, divide the width of the reduced rectangle on the right by the scale factor.
Eric's average income for the first 4 months of the year is $1,450.25, what must be his average income for the remaining 8 months so that his average income for the year is $1,780.75?
Answer:
Average income for the remaining 8 months = $2,111.25
Step-by-step explanation:
Given:
Average income of 4 months = $1,420.25
Annual average income = $1,780.75
Find:
Average income of 8 months
Computation:
⇒ Annual average income = [Average income of 4 months + Average income of 8 months] / 2
⇒ $1,780.75 = [$1,420.25 + Average income of 8 months] / 2
⇒ $3,561.5 = $1,420.25 + Average income of 8 months
⇒ Average income of 8 months = $3,561.5 - $1,420.25
Average income of 8 months = $2,111.25
A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of seven cups of coffee from this machine show the average content to be 7.4 ounces with a standard deviation of 0.70 ounce. Do you think that the machine has slipped out of adjustment and that the average amount of coffee per cup is different from 7 ounces
Answer:
[tex]t=\frac{7.4-7}{\frac{0.7}{\sqrt{7}}}=1.512[/tex]
The degrees of freedom are
[tex]df=n-1=7-1=6[/tex]
And the p value for this case is:
[tex]p_v =2*P(t_{(6)}>1.512)=0.181[/tex]
The p value is a higher value and using a significance levels of 5% or 10% we see that the p value is higher than the significance level and then we FAIL to reject the null hypothesis and we don't have enough evidence to conclude that the true mean is different from 7 ounces.
Step-by-step explanation:
Information provided
[tex]\bar X=7.4[/tex] represent the sample mean
[tex]s=0.7[/tex] represent the sample standard deviation
[tex]n=7[/tex] sample size
[tex]\mu_o 7[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the average amount of coffee per cup is different from 7 ounces, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 7[/tex]
Alternative hypothesis:[tex]\mu \neq 7[/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{7.4-7}{\frac{0.7}{\sqrt{7}}}=1.512[/tex]
The degrees of freedom are
[tex]df=n-1=7-1=6[/tex]
And the p value for this case is:
[tex]p_v =2*P(t_{(6)}>1.512)=0.181[/tex]
The p value is a higher value and using a significance levels of 5% or 10% we see that the p value is higher than the significance level and then we FAIL to reject the null hypothesis and we don't have enough evidence to conclude that the true mean is different from 7 ounces.
Help Please!!!! I mark u brainiiest.
Answer:
Step-by-step explanation:
mode is what number is there the most and range is the highest take the lowest
Answer:
Step-by-step explanation:
mode is what number is there the most and range is the highest take the lowest
Emma and Max want to buy a house together.
Emma earns £18,500 and Max earns £22,500. They have £6000 savings.
They want to buy a house that is being sold for £130,000.
They will pay the deposit with their savings and take out a mortgage to pay for the rest.
Emma and Max can borrow 3 times their combined incomes as a mortgage.
They will need to pay 5% of the selling price of the value as a deposit.
How much can they borrow as a mortgage?
Answer:
£123,000
Step-by-step explanation:
Their combined income is ...
£18,500 +22,500 = £41,000
They can borrow 3 times this amount, or ...
3 × £41,000 = £123,000
__
Comment on this transaction
The required deposit is 5% of 130,000 = 6,500, which is more than their savings. After this down payment is made, the remaining value is £123,500, which exceeds their borrowing power. It appears that Emma and Max need to find a house with a lower price.
and simplify this too
Answer:
-5x^4
Step-by-step explanation:
Cube root of -125 is -5
Cube root of n^12 is n^4
Answer:
3 x (-125n^12)^1/2
Step-by-step explanation:
) Tara earns twice as much per hour as Kayte.
Kayte earns $3 more per hour than Austin. As
a group, they earn $41 per hour. What is
Austin's hourly wage?
Answer:
Austin's hourly wage is $8.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
Tara's hourly wage is x.
Kayte's hourly wage is y.
Austin's hourly wage is z.
Tara earns twice as much per hour as Kayte.
This means that [tex]x = 2y[/tex]
Kayte earns $3 more per hour than Austin.
This means that [tex]y = z + 3[/tex]
As a group, they earn $41 per hour.
This means that [tex]x + y + z = 41[/tex]
What is Austin's hourly wage?
This is z.
[tex]x + y + z = 41[/tex]
[tex]y = z + 3[/tex] and [tex]x = 2y[/tex], so [tex]x = 2(z + 3) = 2z + 6[/tex]
[tex]x + y + z = 41[/tex]
[tex]2z + 6 + z + 3 + z = 41[/tex]
[tex]4z + 9 = 41[/tex]
[tex]4z = 32[/tex]
[tex]z = \frac{32}{4}[/tex]
[tex]z = 8[/tex]
Austin's hourly wage is $8.
Answer:
Austin's hourly wage is $8.
Step-by-step explanation:
We can write this problem as a system of linear equations.
We define T: Tara's hourly wage, A: Austin's hourly wage and K: Kayte's hourly wage.
Then, if Tara earns twice as much per hour as Kayte, we have:
[tex]T=2K[/tex]
If Kayte earns $3 more per hour than Austin, we have:
[tex]K=A+3[/tex]
And if they earn $41 per hour as a group, we know:
[tex]T+K+A=41[/tex]
We can use all equations to replace in the third one, as:
[tex]T+K+A=41\\\\(2K)+K+A=41\\\\3K+A=41\\\\3(A+3)+A=41\\\\3A+9+A=41\\\\4A=41-9=32\\\\A=32/4=8[/tex]
Austin's hourly wage is $8.
OMG THIS QUESTION IS SO HARD WILL RATE IF YOU GET IT
Step-by-step explanation:
idk what is the order of those mesretments. but its 2*s of every 2 opposite rectangles (2*s1+2s2+2s3) that s1 is height*length s2 is length*width and s3 is height*width
The segments are tangents to the circle. Find the perimeter of JLNQ.
The perimeter of the polygon is
Answer:
36 Units.
Step-by-step explanation:
In the diagram attached, K, M, P and R are points of tangency.
Theorem: Tangents to a circle from the same point are equal.
By the theorem above,
LK=LM=6 Units
NM=NP=2 Units
QP=QR=7 Units
JR=JK=3 Units
Therefore:
JL=JK+KL=3+6=9 Units
LN=LM+LN=6+2=8 Units
NQ=NP+PQ=2+7=9 Units
QJ=QR+RJ=7+3=10 Units
Therefore, the perimeter of the polygon JLNQ =9+8+9+10
=36 Units.
Note: The second diagram shows the theorem already applied.
In which table(s) does y vary directly with x? Check all that apply.
2
y
y
X
х
3
y
2
-4
-2
-2
-1
lo
1
3
9
-2
-1
-1
1
0
-1
6
18
2
1
2
-2
1
-2
7
21
6
3
5
-5
2
-3
W
Answer:
see below
Step-by-step explanation:
A relation is "direct variation" if it can be written in the form ...
y = kx
for some constant k. That value can be found from any line* in a table that has direct variation:
k = y/x
_____
* A table with direct variation may have the entry (x, y) = (0, 0). That table entry cannot be used to find the value of k. If either x or y is zero, the other must be also if the variation is direct.
Answer:
first 3
Step-by-step explanation:
tell me if u need an explanation
If your target number of calories is 1200 per day to lose weight, but you are consuming 1100 calories per day, then your target is what percent of the calories you are consuming?
Answer:
109.090909....%(goes on indefinitely)
Step-by-step explanation:
If you are only consuming 1100, and your goal is 1200, as a percentage your target is 1200/1100 of what you are consuming. That simplifies to 12/11, which would mean as a percentage, your target is 109.0909090909...% of what you are consuming.
PLEASE HELP!! I WILL GIVE YOU EVERYTHING
Answer:
Step-by-step explanation:
7.9
Answer:
y - 4 = (-3/2)(x - 4)
Step-by-step explanation:
Here's how we obtain the blue graph:
1) translate the red graph 5 units to the right, and
2) translate the resulting graph 5 units upward.
The equation of the blue graph is y - 4 = (-3/2)(x - 4)
What’s the correct answer for this question?
Answer:
D.
Step-by-step explanation:
In the attached file
pls pls help! ik it’s super simple but i’m slow
James grows corn on 1/4 of his land. If he has 65 acres of land, how much of the
land is used for growing corn?
acres
Answer:
16.25 acres
Step-by-step explanation:
If corn is 1/4 of the land and we have 65 acres, we merely multiply 1/4 to 65.
You get 16.25 acres.
Answer:
16.25acres
Step-by-step explanation:
65/4=16.25 or 16 and 1/4
heeeeeeeelllllllllllllppppppppp plz i need this fast
Answer:
c is true
Step-by-step explanation:
What is f(-2)?
-3
-1
1
3
Answer:
option b
Step-by-step explanation:
b i did it on edge
Evaluate the expression y - x + z for x = 4.7, y = 6, and z=0.68
y – X + z =
(Type an integer or a decimal.)
Answer:
1.98
Step-by-step explanation:
y - x + z for
x = 4.7, y = 6, and z=0.68
6 - 4.7 +.68
1.3+.68
1.98
Answer:
[tex]= 1.98 \\ [/tex]
Step-by-step explanation:
given that,
[tex]x = 4.7 \\ y = 6 \\ z = 0.68[/tex]
Let's solve now
[tex]y - x + z \\ 6 - 4.7 + 0.68 \\ 1.3 + 0.68 \\ = 1.98[/tex]
Find the value of k to the nearest whole number.
Answer:
theres no picture or something for the value of k