AP Stats - Chapter 6 Practice Test

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 given 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?

• 0.1

• 0.4

• 0.8

• 1

• Cannot be determined

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 given probability distribution.

The standard deviation of X is 0.9. Which of the following is the best interpretation of this value?

• About 90% of subjects solved 3 or fewer puzzles.

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

• The typical subject solved an average of 0.9 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

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 given probability distribution.

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?

• 0

• 0.81

• 0.9

• 1.27

• 1.8

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

• X = student's height; Y = student's weight

• X = student's IQ; Y = student's GPA

• X = student's PSAT Math Score; Y = student's PSAT Verbal Score

• X = average amount of homework the student does per night; Y = student's GPA

• X = average amount of homework the student does per night; Y = student's height

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 given day. Assuming that the machine works properly and that no sodas are stolen from the machine, what are the mean and standard deviation of Y?

• $\mu_Y\ =\ \text{1.50, }\sigma_Y\ =\ \text{22.50}$

• $\mu_Y\ =\ \text{1.50, }\sigma_Y\ =\ 33.75$

• $\mu_Y\ =\ \text{75, }\sigma_Y\ =\ 18.37$

• $\mu_Y\ =\ \text{75, }\sigma_Y\ =\ \text{22.50}$

• $\mu_Y\ =\ \text{75, }\sigma_Y\ =\ \text{33.75}$

The weight of tomatoes chosen at random from a bin at the farmer's market follows a Normal distribution with  $\mu\ =\ 10\ ounces\$  and $\sigma\ =\ 1\ ounce$  .  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 2 ounces.

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

• binomial, with mean 40 ounces and standard deviation 2 ounces.

• binomial, with mean 40 ounces and standard deviation 4 ounces.

Which of the following random variables is geometric?

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

• The number of cards I deal from a well-shuffled deck

  of 52 cards until I get a heart.

• The number of digits I read in a randomly selected

  row of the random digits table until I find a 7.

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

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

Seventeen people have been exposed to a particular

disease. Each one independently has a 40% chance

of contracting the disease. A hospital has the capacity

to handle 10 cases of the disease. What is the prob-

ability that the hospital’s capacity will be exceeded?

• 0.011

• 0.035

• 0.092

• 0.965

• 0.989

The figure shows the probability distribution of a

discrete random variable X. Note that the cursor is on

the histogram bar representing a value of 6. Which of

the following best describes this random variable?

• Binomial with n = 8, p = 0.1

• Binomial with n = 8, p = 0.3

• Binomial with n = 8, p = 0.8

• Geometric with p = 0.1

• Geometric with p = 0.2

A test for extrasensory perception (ESP) involves asking a person to tell which of 5 shapes—a circle, star, triangle, diamond, or heart—appears on a hidden computer screen. On each trial, the computer is equally likely to select any of the 5 shapes. Suppose researchers are testing a person who does not have ESP and so is just guessing on each trial.

What is the probability that the person guesses the first 4 shapes incorrectly but gets the fifth correct?

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