Answer:
Tina can select and answer the essay questions on her test in 35 ways.
Step-by-step explanation:
The order in which she chooses the questions is not important. For example, choosing questions 1, 3 and 7 is the same as choosing 7, 3 and 1. So we use the combinations formula to solve this question.
Combinations formula:
[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]
In this question:
Three questions from a set of 7. So
[tex]C_{7,3} = \frac{7!}{3!(7-4)!} = 35[/tex]
Tina can select and answer the essay questions on her test in 35 ways.
Tina can select and answer the essay question on her test in 35 ways.
Number of ways to select 'r' objects out of 'n' objects is given by the expression,
Number of ways = [tex]^nC_r[/tex]
Since, [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
If n = 7 and r = 3,
Number of ways to select 3 essays out of 7 will be,
Number of ways = [tex]^7C_3[/tex]
[tex]=\frac{7!}{3!(7-3)!}[/tex]
[tex]=\frac{7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}[/tex]
[tex]=35[/tex]
Therefore, Tina can select and answer the essay question on her test in 35 ways.
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I’ve been stuck can someone explain
Answer:
Option (3)
Step-by-step explanation:
From the figure attached,
AB and CD are two chords intersecting at O.
m∠AOD = 37°
m∠AOC + m∠AOD = 180° [Since these angles are supplementary angles]
m∠AOC = 180° - 37°
= 143°
By the theorem of intersecting chords,
Measure of angle formed is the half of the sum of measures of the arcs intercepted by the angle and vertical angle.
m∠AOC = [tex]\frac{1}{2}(\widehat{AC}+\widehat{BD})[/tex]
143° = [tex]\frac{1}{2}[(x+5)+(x-5)][/tex]
143° = x
Therefore, Option (3) will be the answer.
f(x) = 2x - 2
Find f(3)
Step-by-step explanation:
Replace x = 3
f(3) = 2(3) - 2
= 6 - 2
= 4
Answer:
f(3) =4
Step-by-step explanation:
f(x) = 2x - 2
Let x=3
f(3) = 2*3 - 2
= 6-2
= 4
a rectangle has an area of 54 square inches and a length of 6 inches. what is the width, in inches, of the rectangle?
Answer:
9 inches
Step-by-step explanation:
For similar problems like this, divide the area by the given length or width. In this case, your equation would be 54/6 = 9.
The width of the rectangle can be found as 9 inch.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The area and length of rectangle are given as 54 inch² and 6 inches.
Suppose the width of the rectangle be x.
Since, the area of rectangle is given as the product of length and breadth, the following equation can be written as,
6x = 54
⇒ x = 54/6
⇒ x = 9
Hence, the width is given as 9 inch.
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Choose the correct answer below. A. The mean MPG of this type of vehicle for 95% of all samples of the same size is contained in the interval. B. 95% of the sample data fall between the limits of the confidence interval. C. We have 95% confidence that the mean MPG of this type of vehicle for the sample is contained in the interval. D. We have 95% confidence that the population mean MPG of this type of vehicle is contained in the interval.
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is
The table below contains the overall miles per gallon (MPG) of a type of vehicle. Complete parts a and b below.
28, 34, 28, 20, 21, 31, 28, 24, 34, 35 , 36, 26, 25, 20
a. Construct a 95% confidence interval estimate for the population mean MPG for this type of vehicle, assuming a normal distribution.
b. Choose the correct answer below.
A. We have 95% confidence that the mean MPG of this type of vehicle for the sample is contained in the interval.
B. We have 95 ℅ confidence that the population mean MPG of this type of vehicle is contained in the interval. This is the correct answer.
C.95 % of the sample data fall between the limits of the confidence interval.Your answer is not correct.
D. The mean MPG of this type of vehicle for 95?% of all samples of the same size is contained in the interval.
Solution:
a) Mean = (28 + 34 + 28 + 20 + 21 + 31 + 28 + 24 + 34 + 35 + 36 + 26 + 25 + 20)/14 = 27.86
Standard deviation = √(summation(x - mean)²/n
n = 14
Summation(x - mean)² = (28 - 27.86)^2 + (34 - 27.86)^2 + (28 - 27.86)^2 + (20 - 27.86)^2 + (21 - 27.86)^2+ (31 - 27.86)^2 + (28 - 27.86)^2 + (24 - 27.86)^2 + (34 - 27.86)^2 + (35 - 27.86)^2 + (36 - 27.86)^2 + (26 - 27.86)^2 + (25 - 27.86)^2 + (20 - 27.86)^2 = 399.7144
Standard deviation = √(399.7144/14) = 5.34
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation = 5.34
n = number of samples = 14
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 14 - 1 = 13
Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05
α/2 = 0.05/2 = 0.025
the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975
Looking at the t distribution table,
z = 2.16
Margin of error = 2.16 × 5.34/√14
= 3.08
The confidence interval is 27.86 ± 3.08
b) B. We have 95 ℅ confidence that the population mean MPG of this type of vehicle is contained in the interval.
To play the game you spin a spinner like the one shown you win if the arrow lands in one of the areas marked Win Lee played this game many times and recorded her results she won 11 times and lost 57 times use lee date to explain how to find the experimental probability of winning this game and to complete the explanation
Answer:
She played the game 11+57 = 68 times. She won 11 times. So the experimental probability of Lee winning is 11/68 = 0.1618 = 16.18%.
Step-by-step explanation:
To find the experimental probability of an outcome we divide:
The number of trials in which the desired outcome happened by the total number of trials.
In this question:
Experimental probability of winning this game.
She played the game 11+57 = 68 times. She won 11 times. So the experimental probability of Lee winning is 11/68 = 0.1618 = 16.18%.
On Saturday, a local hamburger shop sold a combined total of 432 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday
Answer: 268 hamburgers
For the function, find all critical numbers and then use the second-derivative test to determine whether the function has a relative maximum or minimum at each critical number. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x) = x3 − 12x2 + 21x − 8relative maxima x=relative minima x=
Answer:
relative maximum: x = 1
relative minimum: x = 7
Step-by-step explanation:
Critical points:
Values of x for which f'(x) = 0.
Second derivative test:
For a critical point, if f''(x) > 0, the critical point is a relative minimum.
Otherwise, if f''(x) < 0, the critical point is a relative maximum.
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]f(x) = x^{3} - 12x^{2} + 21x - 8[/tex]
Finding the critical points:
[tex]f'(x) = 3x^{2} - 24x + 21[/tex]
[tex]3x^{2} - 24x + 21 = 0[/tex]
Simplifying by 3
[tex]x^{2} - 8x + 7 = 0[/tex]
So [tex]a = 1, b = -8, c = 7[/tex]
[tex]\bigtriangleup = (-8)^{2} - 4*1*7 = 36[/tex]
[tex]x_{1} = \frac{-(-8) + \sqrt{36}}{2} = 7[/tex]
[tex]x_{2} = \frac{-(-8) - \sqrt{36}}{2} = 1[/tex]
Second derivative test:
The critical points are x = 1 and x = 7.
The second derivative is:
[tex]f''(x) = 6x - 24[/tex]
[tex]f''(1) = 6*1 - 24 = -18[/tex]
Since f''(1) < 0, at x = 1 there is a relative maximum.
[tex]f''(7) = 6*7 - 24 = 18[/tex]
Since f''(x) > 0, at x = 7 there is a relative minumum.
WILL MARK BRAINLIEST !!! NEED HELP
Answer:
[tex] y = -\frac{1}{3}x-2[/tex]
Step-by-step explanation:
From the table it is clear that the line is passing through the points [tex] (0,\: -2)= (x_1, \:y_1) \: \&\: (-6, \:0)=(x_2,\:y_2) [/tex]
(There are many other points in the table and any two of them can chosen as per our convenience)
Equation of line in two point form is given as:
[tex] \frac{y-y_1}{y_1 - y_2} = \frac {x-x_1}{x_1 - x_2} \\\\
\therefore \frac{y-(-2)}{-2 - 0} = \frac {x-0}{0 - (-6)} \\\\
\therefore \frac{y+2}{-2} = \frac {x}{0+6)} \\\\
\therefore \frac{y+2}{-2} = \frac {x}{6)} \\\\
\therefore 6(y + 2) = - 2(x)\\
\therefore 6y + 12 = - 2x \\
\therefore 6y = - 2x - 12\\\\
\therefore y = -\frac{2}{6}x-\frac{12}{6}\\\\
\huge \red {\boxed {y = -\frac{1}{3}x-2}} \\\\[/tex]
The 10th grade class at Central high school was surveyed about whether they liked running or swimming. Of those surveyed, 58% said they liked to swim and 36% said they liked to run. If 18% said they liked both swimming and running, what percent of those surveyed liked neither?
Answer:
24% of those surveyed liked neither
Step-by-step explanation:
Set concepts:
We use set concepts to solve this question.
I am going to say that:
P(A) is the percentage of people that liked to swim.
P(B) is the the percentage of people that liked to run.
The percentage of people that liked at least one of these activities is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In which [tex]P(A \cap B)[/tex] is the probability that a person liked both these activities.
The percentage of people that liked neither is:
[tex]P = 1 - P(A \cup B)[/tex]
Of those surveyed, 58% said they liked to swim and 36% said they liked to run.
This means that [tex]P(A) = 0.58, P(B) = 0.36[/tex]
18% said they liked both swimming and running
This means that [tex]P(A \cap B) = 0.18[/tex]
What percent of those surveyed liked neither?
At least one:
[tex]P(A \cup B) = 0.58 + 0.36 - 0.18 = 0.76[/tex]
Neither:
[tex]P = 1 - P(A \cup B) = 1 - 0.76 = 0.24[/tex]
24% of those surveyed liked neither
Pleaseeee Thank you!!!!!!!!!
Answer:
D.
Step-by-step explanation:
Let's solve each choice.
A: 3 divided by 90 is 3/90 and can be simplified to 1/30. So no.
B: 1/5 divided by 6. Recall that when dividing, you multiply the 1st term by the 2nd term's reciprocal. If you do this, you get 1/30. So no.
C: 1/6 divided by 5. Again, multiply 5's reciprocal to 1/6. There you get 1/30. So no.
D: 6 divided by 1/5. Again, multiply 1/5's reciprocal to 6. 1/5's reciprocal is 5. 5*6 = 30. So this is the correct answer.
The following data represent the pulse rates? (beats per? minute) of nine students enrolled in a statistics course. Treat the nine students as a population.Complete parts ?(a) through? (c). Student Pulse ??Perpectual Bempah 64 ??Megan Brooks 77 ??Jeff Honeycutt 89 ??Clarice Jefferson 69 ??Crystal Kurtenbach 89 ??Janette Lantka 65 ??Kevin McCarthy 88 ??Tammy Ohm 69 ??Kathy Wojdya 87(a) Determine the population mean pulse. The population mean pulse is approximately nothing beats per minute. ?(Round to one decimal place as? needed.)(b) Determine the sample mean pulse of the following two simple random samples of size 3. Sample? 1: StartSet Janette comma Clarice comma Megan EndSet Sample? 2: StartSet Perpectual comma Clarice comma Megan EndSet The mean pulse of sample 1 is approximately nothing beats per minute. ?(Round to one decimal place as? needed.) The mean pulse of sample? 2, is approximately nothing beats per minute. ?(Round to one decimal place as? needed.)(c) Determine if the means of samples 1 and 2? overestimate, underestimate, or are equal to the population mean. The mean pulse rate of sample 1 ? (underestimates/ is equal to/ overestimates) the population mean. The mean pulse rate of sample 2 (is equal to/ underestimates/ or overestimates) the population mean.
Answer:
(a)77.4bpm
(b)Mean of Sample 1 = 70.3 beats per minute.
Mean pulse of sample 2 = 70 beats per minute.
(c)
The mean pulse rate of sample 1 underestimates the population mean. The mean pulse rate of sample 2 underestimates the population mean.Step-by-step explanation:
(a)Population mean pulse.
The pulse of the nine students which represent the population are:
Perpectual Bempah 64Megan Brooks 77Jeff Honeycutt 89 Clarice Jefferson 69Crystal Kurtenbach 89 Janette Lantka 65Kevin McCarthy 88Tammy Ohm 69Kathy Wojdya 87[tex]\text{Population Mean} =\dfrac{64+77+89+69+89+65+88+69+87}{9} \\=\dfrac{697}{9} \\\\=77.44[/tex]
The population mean pulse is approximately 77.4 beats per minute.
(b)Sample 1: {Janette,Clarice,Megan}
Janette: 65bpmClarice: 69bpmMegan: 77bpmMean of Sample 1
[tex]\text{Sample 1 Mean} =\dfrac{65+69+77}{3} \\=\dfrac{211}{3} \\\\=70.3[/tex]
Sample 2: {Janette,Clarice,Megan}
Perpetual: 64bpmClarice: 69bpmMegan: 77bpmMean of Sample 2
[tex]\text{Sample 2 Mean} =\dfrac{64+69+77}{3} \\=\dfrac{210}{3} \\\\=70[/tex]
The mean pulse of sample 1 is approximately 70.3 beats per minute.
The mean pulse of sample 2 is approximately 70 beats per minute.
(c)
The mean pulse rate of sample 1 underestimates the population mean. The mean pulse rate of sample 2 underestimates the population mean.A cylindrical tank with a cross-sectional area of 441 cm squared is filled to a depth of 441 cm with water. At tequals0, a drain in the bottom of the tank with an area of 21 cm squared is opened, allowing water to flow out of the tank. The depth of water in the tank at time tgreater than or equals0 is d(t)equals(21 minus 1.1 t )squared.
At what time is the tank empty?
A line has an equation of y = - 3x + 8. What is the y-intercept of the line? Please enter your answer as a coordinate (x, y). *
Answer:
(0, 8).
Step-by-step explanation:
The y intercept occurs when = 0, so we have the equation:
y = -3(0) + 8
y = 0 + 8
y = 8.
The answer is (0, 8).
Question 1:Lauren wants to buy 3 shirts at $15.00 each. At home, she calculates the total cost as $46.20, using the sales tax of 8%. At the store, Lisa (the cashier) tells Lauren the total cost is $48.60. Which person is wrong, Lauren or Lisa
Question 2:What’s the cost of the shirts before tax
Question 3:How much is the sales tax for all shirts
Question 4:What is the total cost of the shirts, including tax?
Answer:
Lauren is wrong
Step-by-step explanation:
1. Lauren is wrong
2. What’s the cost of the shirts before tax
Each shirt cost $15 and the total = $15 x 3 = $45
3. How much is the sales tax for all shirts
Sale tax for all shirts is $45 x 0.08 = $3.6
4. What is the total cost of the shirts, including tax?
Total cost = $45 + $3.6 = $48.60
Identify the graph of the equation. What is the angle of rotation for the equation?
y2 + 8x = 0
hyperbola; 30°
b. parabola; 90°
a.
C.
d.
hyperbola; 180°
parabola; 0°
Answer:
D. Parabola; 0°
Step-by-step explanation:
Suppose that in a certain sinkhole the ground dropped 69.6 ft in 24 hr. Find the unit rate representing the change in altitude per hour ..the unit rate representing the change in altitude is how many feet per hour
Answer:
2.9 per hour
Step-by-step explanation:
Divide 69.9 by 24
Mr. Evans is considering offering a second after-school tutoring session for his math students each week. He records the number of
students who attend his current sessions each week. The results from the last twelve weeks are shown in the dot plot below.
+
1 2
+
0
+
3
4 5 6 7 8 9 10 11 12 13 14 15
Number of Students
Which statement properly describes the data?
There is not enough information to determine if the data is skewed.
O
The data is symmetric.
The data is skewed right.
The data is skewed left.
Answer:
Step-by-step explanation:
the data is skewed left
The data in the given set is skewed towards left because the mean of the data is 7.5 and the data is not distributed symmetrically in the given set. Thus, the correct option is C.
What is a Skewed data set?Skewed data is the data which creates an asymmetrical, skewed curve on the graph scale. In statistics, the graph of a data set with normal distribution is symmetrical and has a bell-like shape. However, the skewed data has a tail on either side of the graph as well.
Skewness can be demonstrated on a bell curve when the data points are not distributed symmetrically to the left and right sides of the median on the curve. If the bell curve is shifted to the left or towards the right side, it is said to be skewed curve. The two halves of the distribution are not mirror images in the skewed curve because the data are not distributed equally on both sides of the distribution peak.
Therefore, the correct option is C.
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if a quadratic equation with real coefficients has a discriminant of -36 then what type of roots does it have
Step-by-step explanation:
We have,
If a quadratic equation with real coefficients has a discriminant of -36.
The general form of quadratic equation is :
[tex]ax^2+bx+c=0[/tex]
The discriminant of this equation is : [tex]D=b^2-4ac[/tex]
If D=0, it will have 1 real roots
If D>0, it will have 2 real roots
If D<0, it will have no real roots
We have,
D = -36 < 0, so, the quadratic equation will have no real roots.
can the square root of a rational number be irrational?
Answer:
Yes. Some examples are √2, √3, √5.
You better believe it ! In fact, if you don't count an infinite number of examples, you'll find that MOST of their square roots are irrational.
Let's examine the smallest 1,000 integers . . .
-- They're all rational numbers, but ...
-- only 31 of them have rational square roots !
The elephant is in danger of being completely wiped out. What sort of species is
an elephant?
a limiting species
O
an extinct species
a threatened species
an endangered species
Answer:
Endangered species
Step-by-step explanation:
An endangered species is a species that is at risk of extinction due to rapid decrease in their population .Their decrease in population might be due to loss of habitat and genetic variation. The loss of habitat might be due to natural factors like the climate change For example animals like dinosaurs during the cretaceous period that experience rapid change in the climate loss their habitat and went extinct.
Human activity can also influence loss of habitat. Development in housing , agriculture and industry can also threaten the habitats of native organisms. The loss of their habitat might cause sudden extinction of these organisms. They might find it hard to adapt to another environment or even procreate.
Generally, endangered species are species that are threatened by extinction. Elephants that are in danger of been wiped out is an endangered species.
A person must pay $ $ 8 to play a certain game at the casino. Each player has a probability of 0.21 of winning $ $ 14, for a net gain of $ $ 6 (the net gain is the amount won 14 minus the cost of playing 8). Each player has a probability of 0.79 of losing the game, for a net loss of $ $ 8 (the net loss is simply the cost of playing since nothing else is lost). What is the Expected Value for the player (that is, the mean of the probabiltiy distribution)? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer with two decimal places.
Answer:
-$5.06
Step-by-step explanation:
Given the probability distribution of X where X is the net gain or loss
[tex]\left|\begin{array}{c|c|c}Profit(X)&\$6&-\$8\\P(X)&0.21&0.79\end{array}\right|[/tex]
The expected value of X is defined as follows:
Expected Value of X, [tex]E(X)=\sum_{i=1}^nx_iP(x_i)[/tex]
Therefore, the expected value of the player
E(X)=(6*0.21)+(-8*0.79)
=1.26-6.32
[tex]E(X)=-\$5.06[/tex]
The expected value of each player at the casino is -$5.06.
which choice is equivalent to the fraction below?
Answer: 2 ÷ 17
Step-by-step explanation: When you have something in this form, a/b, it means the same thing as a divided by b.
So 2/17 means the same thing as 2 ÷ 17.
Un bosque de 2 km2 está formado por hayas y pinos. Las hayas ocupan 380.000 m2 ¿Cuántos metros cuadrados ocupan los pinos?
Answer:
Los pinos ocupan [tex] \\ 1620000m^{2}[/tex] o 1 millón seiscientos veinte mil metros cuadrados.
Step-by-step explanation:
Una manera de resolver este problema es la siguiente:
[tex] \\ 1km^{2} = 1km * 1km = 1000m * 1000m = 1000000m^{2}[/tex]
[tex] \\ 2km^{2} = 2km * 1km = 2000m * 1000m = 2000000m^{2} = 2 * 10^{6}m^{2}[/tex]
En palabras, [tex] \\ 2km^{2} = 2000000m^{2}[/tex], o dos kilómetros cuadrados son iguales a 2 millones de metros cuadrados.
Sabemos que:
Estos [tex] \\ 2km^{2} = 2000000m^{2}[/tex] de bosque lo ocupan hayas y pinos, y, adicionalmente, Las hayas ocupan [tex] \\ 380000m^{2}[/tex].De esta manera, la parte que ocupan los pinos es el total del bosque menos el área ocupada por las hayas. Por lo tanto, el área ocupada por los pinos es:
[tex] \\ 2000000m^{2} - 380000m^{2}[/tex]
[tex] \\ 1620000m^{2}[/tex]
¿Cuántos metros cuadrados ocupan los pinos?
Los pinos ocupan, entonces, [tex] \\ 1620000m^{2}[/tex] o 1 millón seiscientos veinte mil metros cuadrados.
A MP3 Manufacturer claims that 65% of teenagers have their own MP3 player. A researcher wishes to test the claim and selects a random sample of 80 teenagers. She finds that 57 have their MP3 player. At a .05 significance level, should the claim be rejected? Please show work.
Answer:
Null hypothesis: H0 = 0.65
Alternative hypothesis: Ha ≠ 0.65
z = 1.172
P value = P(Z≠1.172) = 0.24
Decision we fail to reject the null hypothesis. That is, there is convincing evidence enough to reject the Null hypothesis.
Rule
If;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
Z score > Z(at 95% confidence interval) ---- reject Null hypothesis
Z score < Z(at 95% confidence interval) ------ accept Null hypothesis
Step-by-step explanation:
Given;
n=80 represent the random sample taken
Null hypothesis: H0 = 0.65
Alternative hypothesis: Ha ≠ 0.65
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size = 80
po = Null hypothesized value = 0.65
p^ = Observed proportion = 57/80 = 0.7125
Substituting the values we have
z = (0.7125-0.65)/√(0.65(1-0.65)/80)
z = 1.17201807734
z = 1.172
To determine the p value (test statistic) at 0.05 significance level, using a two tailed hypothesis.
P value = P(Z≠1.172) = 0.241197 = 0.24
Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = 1.172) which falls within the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.24 which is higher than 0.05. Then we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is valid.
If the average ago of retirement for a random sample of 87 retired persons is 66 years with a standard deviation of 2 years.a. b. c. d.e.f.g. Find the probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more. Find all values to 3 decimal places.
Answer:
0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.
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:
[tex]\mu = 66, \sigma = 2, n = 87, s = \frac{2}{\sqrt{87}} = 0.214[/tex]
Find the probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.
This probability is 1 subtracted by the pvalue of Z when X = 66.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{66.5 - 66}{0.214}[/tex]
[tex]Z = 2.336[/tex]
[tex]Z = 2.336[/tex] has a pvalue of 0.99.
1 - 0.99 = 0.01
0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.
graph of y=- 3x+2 is:
Answer:
GRAPH OF 3X+2 IS 6
Step-by-step explanation:
Answer:
The graph below
Step-by-step explanation:
Data from the U.S. Department of Education indicates that 46% of business graduate students from private universities had student loans. Suppose you randomly survey a sample of graduate business students from private universities. Consider the sampling distribution (sample size n = 215) for the proportion of these students who have loans.What is the mean of this distribution?What is the standard deviation of this sampling distribution (i.e., the standard error)?
Answer:
For this case the mean is given by:
[tex] \mu = p =0.46[/tex]
And the standard deviation would be:
[tex] \sigma = \sqrt{\frac{0.46*(1-0.46)}{215}}= 0.0340[/tex]
Step-by-step explanation:
For this case we have the following info given :
[tex] n = 215[/tex] represent the sample size
[tex]p = 0.46[/tex] represent the proportion of business graduate students from private universities had student loans
For this case we want to find the distribution for the sample proportion and we know that this distribution is given by:
[tex] \hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]
And for this case the mean is given by:
[tex] \mu = p =0.46[/tex]
And the standard deviation would be:
[tex] \sigma = \sqrt{\frac{0.46*(1-0.46)}{215}}= 0.0340[/tex]
Answer:
The mean of this distribution is 0.46 and the standard deviation is 0.034.
Step-by-step explanation:
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.
For sampling distributions of samples of size n of a proportion p, the mean is [tex]\mu = p[/tex] and the standard deviation is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]n = 215, p = 0.46[/tex]
So
[tex]\mu = 0.46, s = \sqrt{\frac{0.46*0.54}{215}} = 0.0340[/tex]
The mean of this distribution is 0.46 and the standard deviation is 0.034.
The average cost of producing a single bicycle based on the total number of bicycles produced, x, is represented by this function:f(x)=800+30,000/xUse the drop-down menus to complete the statements to show the difference between the mathematical and reasonable ranges. The reasonable range includes the set of A whole number, B rational numbers,C integers, D real numbers where 800 < y ≤ , A 801, B 30,000, C 30,800, D 24,000,000 while the mathematical range includes the set of A whole numbers,B rational numbers C integers D real numbers and only excludes the value . A 0, B 800, C 30,800
Answer:
The correct answers are B, C, D, B
Step-by-step explanation:
These answers complete the statements that show the difference between the mathematical and reasonable ranges. Good luck! :)
B) Rational Numbers
C) 30,800
D) Real Numbers
B) 800
Correct on edge2020!
Answer:
BCDB
Step-by-step explanation:
What is the simplified form of this expression?
Answer:
[tex]=13x+5[/tex]
Step-by-step explanation:
[tex]\left(2x+9\right)+\left(11x-4\right)\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=2x+9+11x-4\\\mathrm{Group\:like\:terms}\\=2x+11x+9-4\\\mathrm{Add\:similar\:elements:}\:2x+11x=13x\\=13x+9-4\\\mathrm{Add/Subtract\:the\:numbers:}\:9-4=5\\=13x+5[/tex]
Hurry please! I really need help For what value of the variable is the value of 3−5c one less than the value of 1−c?
Answer:
Any values that is greater than 1/2.
Step-by-step explanation:
You have to form an inequality. Given that what values is added to c will satisfy that 3 - 5c is less than 1 - c :
[tex]3 - 5c < 1 - c[/tex]
Next, you have to solve :
[tex] - 5c + c < 1 - 3[/tex]
[tex] - 4c < - 2[/tex]
[tex]c > \frac{ - 2}{ - 4} [/tex]
[tex]c > \frac{1}{2} [/tex]