AP Stats Chapter 6 Practice Test

AP Stats Chapter 6 Practice Test

11th Grade

10 Qs

quiz-placeholder

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AP Stats Chapter 6 Practice Test

AP Stats Chapter 6 Practice Test

Assessment

Quiz

Mathematics

11th Grade

Practice Problem

Medium

CCSS
HSS.MD.A.3, HSS.MD.A.2, HSS.CP.A.2

+2

Standards-aligned

Created by

Ryan Wolf

Used 19+ times

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Media Image

A psychologist studied the number of puzzles that subjects were able to solve in a 5-minute period while listening to soothing music. Let 𝑋 be the number of puzzles completed successfully by a randomly chosen subject. The psychologist found that 𝑋 had the following probability distribution. What is the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music?

Cannot be determined

0.1

0.8

1

0.4

Answer explanation

𝜇𝑋=∑𝑥𝑖𝑝𝑖 then sum up the probabilities that are greater than 𝐸(𝑋).

The expected number of puzzles is 𝐸(𝑋) = 2.3. 𝑃(𝑋>2.3)=0.3+0.1=0.4

Tags

CCSS.HSS.MD.A.2

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Media Image

A psychologist studied the number of puzzles that subjects were able to solve in a 5-minute period while listening to soothing music. Let 𝑋 be the number of puzzles completed successfully by a randomly chosen subject. The psychologist found that 𝑋 had the following probability distribution. The standard deviation of 𝑋 is 0.9. Which of the following is the best interpretation of this value?

About 68% of subjects solved between 0.9 puzzles less and 0.9 puzzles more than the mean.

About 90% of subjects solved 3 or fewer puzzles.

The number of puzzles solved by subjects typically differed from the mean by about 0.9 puzzles.

The number of puzzles solved by subjects typically differed from one another by about 0.9 puzzles.

The typical subject solved an average of 0.9 puzzles.

Answer explanation

The Empirical rule only applies when the distribution is approximately Normal.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Media Image

A psychologist studied the number of puzzles that subjects were able to solve in a 5-minute period while listening to soothing music. Let 𝑋 be the number of puzzles completed successfully by a randomly chosen subject. The psychologist found that 𝑋 had the following probability distribution. The standard deviation of 𝑋 is 0.9. Let 𝐷 be the difference in the number of puzzles solved by two randomly selected subjects in a 5-minute period. What is the standard deviation of 𝐷?

1.8

0.81

0

1.27

0.9

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Suppose a student is randomly selected from your school. Which of the following pairs of random variables are most likely independent?

1.8𝑋 = average amount of homework the student does per night; 𝑌 = student’s GPA

0.81𝑋 = student’s height; 𝑌 = student’s weight

𝑋 = student’s PSAT Math score; 𝑌 = student’s PSAT Verbal score

𝑋 = student’s IQ; 𝑌 = student’s GPA

0.9𝑋 = average amount of homework the student does per night; 𝑌 = student’s height

Answer explanation

The student's height is not affected by the amount of homework he or she does per night.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles 𝑋 bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable 𝑌 equal the total revenue from this machine on a randomly selected day. Assume that the machine works properly and that no sodas are stolen from the machine.

What are the mean and standard deviation of 𝑌?

𝜇𝑌 = $75,

𝜎𝑌 = $18.37

𝜇𝑌 = $75,

𝜎𝑌 = $22.50

𝜇𝑌 = $1.50,

𝜎𝑌 = $22.50

𝜇𝑌 = $75,

𝜎𝑌 = $33.50

𝜇𝑌 = $1.50,

𝜎𝑌 = $33.75

Answer explanation

Y=1.5X and we multiply the mean and standard deviation by 1.5 to obtain the mean and standard deviation of 𝑌.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The weight of tomatoes chosen at random from a bin at the farmer’s market follows a Normal distribution with mean 𝜇 = 10 ounces and standard deviation 𝜎 = 1 ounce. Suppose we pick four tomatoes at random from the bin and find their total weight 𝑇. The random variable 𝑇 is

Normal, with mean 10 ounces and standard deviation 1 ounce.

Normal, with mean 40 ounces and standard deviation 4 ounces.

Binomial, with mean 40 ounces and standard deviation 2 ounces.

Normal, with mean 40 ounces and standard deviation 2 ounces.

Binomial, with mean 40 ounces and standard deviation 4 ounces.

Answer explanation

Remember that you must find the square root of the variance after adding the variances!

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following random variables is geometric?

The number of digits I read in a randomly selected row of the random digits table to get a 7

The number of cards I deal from a well-shuffled deck of 52 cards to get a heart

The number of 7s in a row of 40 random digits

The number of 6s I get if I roll a die 10 times

The number of times I have to roll a single die to get two 6s

Answer explanation

The trials are not independent as the cards are not put back after dealing.

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