AP Stats - Combining Random Variables

Data were collected on the ages, in years, of the men and women enrolled in a large sociology course. Let the random variables M and W represent the ages of the men and women, respectively. The distribution of M has mean 20.7 years and standard deviation 1.73 years. The distribution of W has mean 20.2 years and standard deviation 1.60 years. Of all of those enrolled in the course, 54 percent are men and 46 percent are women. What is the mean age of the combined distribution of both men and women in the course?

• 20.2 years

• 20.43 years

• 20.45 years

• 20.47 years

• 20.50 years

The random variable X has mean 12 and standard deviation 3. The random variable W is defined as W=7+2X. What are the mean and standard deviation of W?

• The mean is 24, and the standard deviation is 6.

• The mean is 24, and the standard deviation is 13.

• The mean is 31, and the standard deviation is 3.

• The mean is 31, and the standard deviation is 6.

• The mean is 31, and the standard deviation is 13.

The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S has mean 7 and standard deviation 3. If R and S are independent, what are the mean and standard deviation of the distribution of R − S?

• Mean 3 and standard deviation 1

• Mean 3 and standard deviation 5

• Mean 3 and standard deviation 7

• Mean 17 and standard deviation 1

• Mean 17 and standard deviation 5

The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S has mean 7 and standard deviation 3. If R and S are independent, what are the mean and standard deviation of the distribution of R + S?

• Mean 3 and standard deviation 1

• Mean 3 and standard deviation 5

• Mean 3 and standard deviation 7

• Mean 17 and standard deviation 1

• Mean 17 and standard deviation 5

Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15. If the customer rolls the dice and rents a second movie every Thursday for 20 consecutive weeks, what is the total amount that the customer would expect to pay for these second movies?

• $0.45

• $0.47

• $0.67

• $3.00

• $9.40

A box contains 10 tags, numbered 1 through 10, with a different number on each tag. A second box contains 8 tags, numbered 20 through 27, with a different number on each tag. One tag is drawn at random from each box. What is the expected value of the sum of the numbers on the two selected tags?

• 13.5

• 14.5

• 15.0

• 27.0

• 29.0

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 random variable X has a mean of 120 and a standard deviation of 15. A random variable Y has a mean of 100 and a standard deviation of 9. If X and Y are independent, approximately what is the standard deviation of X - Y ?

• 17.49

• 24.0

• 12.51

• 20.38

• 6.0

The random variable X is normally distributed with mean 5 and standard deviation 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y ?

• The mean is 20 and the standard deviation is 102.

• The mean is 20 and the standard deviation is 50.

• The mean is 22 and the standard deviation is 102.

• The mean is 22 and the standard deviation is 100.

• The mean is 22 and the standard deviation is 50.

A company sells concrete in batches of 5 cubic yards. 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