AP Stats Chapter 6 Retake Test

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.

Which of the following probability distributions of a discrete random variable X is a legitimate probability distribution?

• 
• 
• 
• None are legitimate

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

Let Z = the number students in Mr. Rooney's English class who arrive late on a randomly selected day. The expected value of Z is 2. Which one of the following is the best interpretation of what this means?

• We can be confident that at least 2 students will be late to Mr. Rooney's class on a randomly selected day.

• On average, the number of students who are late to Mr. Rooney's class on a randomly selected day is 2.

• There are 2 students in Mr. Rooney's class who almost always arrive late.

• 2 students never show up to school.

Let X = the number of times that a randomly selected customer visits a grocery store during a one-week period. Suppose that the probability distribution of X is as listed above.

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

A set of 10 playing cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly, and we draw 4 cards one at a time and without replacement. Let X = the number of red cards drawn. The random variable X has which of the following probability distributions?

• binomial distribution with parameters

  n = 10 and p = 0.5

• binomial distribution with parameters

  n = 4 and p = 0.5

• geometric distribution with parameters

  p = 0.5

• none of the above