Chapter 6 Review

A player pays $15 to play a game in which a chip is randomly selected from a bag of chips. The bag contains 10 red chips, 4 blue chips, and 6 yellow chips. The player wins $5 if a red chip is selected, $10 if a blue chip is selected, and $20 if a yellow chip is selected. Let the random variable X represent the amount won from the selection of the chip, and let the random variable W represent the total amount won, where W=X−15. What is the mean of W ?

• -$4.50

• $10.50

• $4.50

• -$6.50

Tags

CCSS.HSS.MD.B.5A

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.

Question

If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total amount paid for these second movies will exceed $15.00?

• 0

• 0.9

• .14

• .86

Tags

CCSS.HSS.ID.A.4

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.

Question

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

• $0.67

• $3.00

• $9.40

Tags

CCSS.HSS.MD.A.2

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

At a certain bakery, the price of each doughnut is $1.50. Let the random variable D represent the number of doughnuts a typical customer purchases each day. The expected value and variance of the probability distribution of D are 2.6 doughnuts and 3.6 (doughnuts)², respectively. Let the random variable P represent the price of the doughnuts that a typical customer purchases each day. Which of the following is the standard deviation, in dollars, of the probability distribution of P ?

• 1.5(3.6)

• 1.5(2.6)

The quality control manager at a factory records the number of equipment breakdowns each day. Let the random variable Y represent the number of breakdowns in one day. The standard deviation of Y is 0.28. Which of the following is the best interpretation of the standard deviation?

• The number of breakdowns on a randomly selected day is expected to be 0.28.

• The number of breakdowns on a randomly selected day will be 0.28 away from the mean.

• The average number of breakdowns per day for a random sample of days is expected to be 0.28.

• On average, the number of breakdowns per day varies from the mean by about 0.28.

A magazine has 1,620,000 subscribers, of whom 640,000 are women and 980,000 are men. Thirty percent of the women read the advertisements in the magazine and 50 percent of the men read the advertisements in the magazine. A random sample of 100 subscribers is selected. What is the expected number of subscribers in the sample who read the advertisements?

• 30

• 40

• 42

• 50

Tags

CCSS.7.SP.A.2

Consider a data set of positive values, at least two of which are not equal. Which of the following sample statistics will be changed when each value in this data set is multiplied by a constant whose absolute value is greater than 1?

1)The mean

2)The median

3)The standard deviation

• 1 only

• 2 and 3 only

• 1 and 2 only

• 1, 2, and 3

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 ?

• 24

• 17.5

• 12

• 6

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