AP Stat Unit 4 Progress Check: MCQ Part B

The following table shows the probability distribution for the prize amounts that will be awarded at a school raffle. Let the random variable P represent a randomly selected prize amount. What is the expected value of P ?

$3.90

The random variable X takes on the values of 2, 5, n, and 15. The probability distribution of X is shown in the following table. The expected value of X is 9.1. What is the value of n ?

12

Let the random variable X represent the amount of money won or lost for a player who pays $1 to play a certain carnival game. The following table shows the probability distribution of X. Which of the following statements is the best interpretation of the mean of X ?

In the long run, a player will lose an average of $0.15 per carnival game played.

Let random variable S represent the age of the attendees at a local concert. The following histogram shows the probability distribution of the random variable S. Alfonso claims that the distribution of S is symmetric with a mean age of 36. Does the histogram support Alfonso's claim?

No, the distribution is skewed to the left with a mean age greater than 36.

No, the distribution is skewed to the left with a mean age greater than 36. Andromeda claims the distribution of X is skewed to the right with mean equal to 4 movies. Is Andromeda's claim supported by the table?

No, the distribution is skewed to the right with mean less than 4 movies.

The following table shows the joint distribution of random variables X and Y. Which of the following statements about the random variables X and Y is correct?

XX and YY are independent because knowing the value of XX does not change the probability distribution of YY.

Julio sells computers at an electronics store. Let the random variable C represent the number of computers that Julio sells in one week. The following table shows the probability distribution of C. Julio earns $800 per week, with a commission of $200 per computer sold. What is the expected value of Julio's earnings for one week?

$1,462

While investigating customer complaints, the customer relations department of Sonic Air found that 15 percent of the flights arrive early and 25 percent arrive on time. Additionally, 65 percent of the flights are overbooked, and 72 percent are late or not overbooked. One Sonic Air flight will be selected at random. What is the probability that the flight selected will be late and not overbooked?

0.23

Let the random variable X represent the number of people living in a household in a certain town. The standard deviation of X is 1.8. Which of the following statements is the best interpretation of the standard deviation?

On average, the number of people living in a household varies from the mean by about 1.8 people.

Given independent events A and B such that P(A)=0.3 and P(B)=0.5, which of the following is a correct statement?

P(A∪B)=0.65

The distribution of weights of African bush elephants is skewed to the right with mean 6.42 tons and standard deviation 1.07 tons. Let the random variable W represent the weight, in tons, of a randomly selected elephant. The weight is converted to kilograms using the formula Y=900W. Which of the following best describes the distribution of Y ?

Skewed to the right with mean 5,778 kilograms and standard deviation 963 kilograms

Let random variable Q represent the number of employees who work at a certain restaurant on a given day. The following table shows the probability distribution of the random variable Q. Which of the following claims is best supported by the table?

The mean number of employees who work on a given day is less than the median number of employees who work on a given day.

A hockey all-star game has the Eastern Division all-stars play against the Western Division all-stars. On the Eastern Division team there are 8 United States-born players, 14 Canadian-born players, and 2 European-born players. On the Western Division team there are 12 United States-born players, 8 Canadian-born players, and 4 European-born players. If one player is selected at random from the Eastern Division team and one player is selected at random from the Western Division team, what is the probability that neither player will be a Canadian-born player?

160/576

At a large university, data were collected on the number of sisters and brothers that each student had. Let the random variable X represent the number of sisters and the random variable Y represent the number of brothers. The distribution of X has mean 1.00 and standard deviation 0.94. The distribution of Y has mean 1.07 and standard deviation 1.04. What is the mean of the distribution of X+Y ?

2.07

A local amusement park has 30 rides that park visitors can go on. The following table shows the relative frequency distribution for the number of rides that a park visitor will typically go on during one day at the park. The table also shows the deviation, or difference, from 21, the mean of the distribution. Which of the following is closest to the standard deviation of the distribution?

5.83

Parker has a part-time job picking apples. Let the random variable A represent the number of baskets of apples picked each day. The distribution of A has mean 4.5 baskets and standard deviation 1.3 baskets. Parker is paid $65 per day plus $5 per basket. What are the mean μ and standard deviation σ of Parker's daily pay?

B μ=$87.50μ=$87.50 and σ=$6.50

The random variable W can take on the values of 0, 1, 2, 3, or 4. The expected value of W is 2.8. Which of the following is the best interpretation of the expected value of random variable W ?

For values of WW repeatedly selected at random from the distribution, the mean of the selected values will approach 2.8

Biologists are analyzing soil to check for the number of worms and grubs in a wildlife preserve. Let the random variable W represent the number of worms found in 1 square foot of soil, and let the random variable G represent the number of grubs found in 1 square foot of soil. The following tables show the probability distributions developed by the biologists for W and G. Assume that the distributions of worms and grubs are independent. What are the mean, μ, and standard deviation, σ, for the total number of worms and grubs in 1 square foot of soil?

μ=5.28μ=5.28 and σ=1.67σ=1.67