Random variables-Chap 6-MC

Which of the following graphs represents a binomial distribution with n = 20 and p = 0.25?

• Graph A

• Graph B

• Graph C

• Graph D

• Graph E

Two friends, Andy and Bob, participate in a game of bowling every week. From past experiences, it is known that both friends' scores are approximately normally distributed, where Andy has a mean score of 150 with a standard deviation of 30, and Bob has a mean score of 165 with a standard deviation of 15. Assuming that their scores are independent, which of the following values is closest to the probability that Andy will have a greater score than Bob in a single game?

• 0.16

• 0.28

• 0.31

• 0.33

• 0.37

A company sells concrete in batches of 5 cubic yards. The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table below. X = the number of cubic yards: 10, 15, 20, 25, 30 Probability: 0.15, 0.25, 0.25, 0.30, 0.05 The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by Y = 75X - 100. What is the standard deviation of Y?

• $332.00

• $432.00

• $532.00

• $1,343.75

• $1,400.00

An urn contains exactly three balls numbered 1, 2, and 3, respectively. Random samples of two balls are drawn from the urn with replacement. The average, X̄ = (X₁ + X₂) / 2, where X₁ and X₂ are the numbers on the selected balls, is recorded after each drawing. Which of the following describes the sampling distribution of X̄?

• X̄: 1, 1.5, 2, 2.5, 3; Probability: 1/3, 1/3, 1/3, 1/3, 1/3

• X̄: 1, 1.5, 2, 2.5, 3; Probability: 1/9, 2/9, 1/3, 2/9, 1/9

• X̄: 1, 1.5, 2, 2.5, 3; Probability: 0, 0, 1, 0, 0

• X̄: 1, 1.5, 2, 2.5, 3; Probability: 1/10, 1/10, 3/10, 1/10, 1/10

• It cannot be determined from the information given.

Julie generates a sample of 20 random integers between 0 and 9 inclusive. She records the number of 6's in the sample. She repeats this process 99 more times, recording the number of 6's in each sample. What kind of distribution has she simulated?

• The sampling distribution of the sample proportion with n = 20 and p = 0.6

• The sampling distribution of the sample proportion with n = 100 and p = 0.1

• The binomial distribution with n = 20 and p = 0.1

• The binomial distribution with n = 100 and p = 0.1

• The binomial distribution with n = 20 and p = 0.6

Random variable X is normally distributed with mean 10 and standard deviation 3, and random variable Y is normally distributed with mean 9 and standard deviation 4. If X and Y are independent, which of the following describes the distribution of Y - X?

• Normal with mean 1 and standard deviation -1

• Normal with mean -1 and standard deviation 1

• Normal with mean -1 and standard deviation 5

• Normal with mean 1 and standard deviation 7

• Normal with mean -1 and standard deviation 7

The number of sweatshirts a vendor sells daily has the following probability distribution. If each sweatshirt sells for $25, what is the expected daily total dollar amount taken in by the vendor from the sale of sweatshirts?

• $5.00

• $7.60

• $35.50

• $38.00

• $75.00

Let $ X $ represent the number on the face that lands up when a fair six-sided number cube is tossed. The expected value of $ X $ is 3.5, and the standard deviation of $ X $ is approximately 1.708. Two fair six-sided number cubes will be tossed, and the numbers appearing on the faces that land up will be added. Which of the following values is closest to the standard deviation of the resulting sum?

• 1.708

• 1.848

• 2.415

• 3.416

• 5.835

A nonprofit organization plans to hold a raffle to raise funds for its operations. A total of 1,000 raffle tickets will be sold for $1.00 each. After all the tickets are sold, one ticket will be selected at random and its owner will receive $50.00. The expected value for the net gain for each ticket is $-0.95$. What is the meaning of the expected value in this context?

• The ticket owners lose an average of $0.05 per raffle ticket.

• The ticket owners lose an average of $0.95 per raffle ticket.

• Each ticket owner will lose $0.95 per raffle ticket.

• A ticket owner would have to purchase 19 more tickets for the expected value of his or her net gain to increase to $0.00.

• A ticket owner has a 95 percent chance of having a ticket that is not selected.

In the town of Tower Hill, the number of cell phones in a household is a random variable $ W $ with the following distribution: The probability that a randomly-selected household has at least two cell phones is

• 0.20

• 0.25

• 0.55

• 0.70

• 0.80