AP Stats Chapter 5 Exam

Consider the above five sets of outcomes from random phenomena. Which of the above are continuous random variables?

• II and III only

• II and V only

• I and III

• None of these are continuous random variables.

In a particular game, a single card is randomly chosen from a box that contains 3 red cards, 1 green card, and 6 blue card. If a red card is selected, you win $2. If a green card is selected, you win $4. If a blue card is selected, you lose $1. Let X be the amount that you win. The expected value of X is

• $0.40

• $1.00

• $1.60

• $1.40

Determine the probability that a randomly chosen customer visits the grocery store at least twice during a one-week period.

• 0.9

• 0.7

• 0.6

• 0.5

The time in minutes X that you must wait before a train arrives at your local subway station is a uniformly distributed random variable that takes on values between 5 minutes and 15 minutes. That is, the density curve of the distribution of X has constant height between X = 5 and X = 15 and height 0 outside this interval. Determine P(6 < x < 8).

• 0.5

• 0.3

• 0.2

• 0.1

If X and Y are random variables, and Z = X + Y, which of the following is a condition for calculating VARIANCE of Z by using the sum of the VARIANCE of X and Y ?

• X and Y are both normally distributed.

• X and Y are independent.

• X and Y are mutually exclusive.

• All of the above

The weight of a medium-sized orange selected at random from a large bin of oranges at a local supermarket is a random variable with mean μ = 12 ounces and standard deviation σ = 1.2 ounces. Suppose we independently select two oranges at random from the bin. The difference in the weights of the two oranges (the weight of the first orange minus the weight of the second orange) is a random variable with a standard deviation equal to:

• 0 ounces

• 1.50 ounces

• 1.70 ounces

• 2.40 ounces

The daily total sales (excluding Saturday) at a small restaurant has a probability distribution that is approximately Normal with a mean of μ = $530 and a standard deviation of σ = $120. The probability the sales will exceed $700 on a given day is approximately

• 0.9222

• 0.5578

• 0.0778

• 0.0125

There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The student's expected (mean) score on this exam is

• 5

• 15

• 25

• 50

There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The standard deviation of the student's score on the exam is

• 1.94

• 4.33

• 9.68

• 21.65

In a certain large population, 70% are right-handed. You need a left-handed pitcher for your softball team and decide to find one by asking people chosen from the population at random. (We assume that once you do find a left-hander, he or she will be happy to join your team and will say yes.) Which of the following is closest to the probability that you will have to ask four or more people before finding your first left-hander?

• 0.103

• 0.657

• 0.343

• 0.027