Ch 6 (Random Variables) MC Review

A marketing survey compiled data on the number of cars in households. If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the following probability distribution (see below).

What is the probability that a randomly chosen household has at least two cars?

• 0.19

• 0.20

• 0.29

• 0.39

• 0.61

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

What is the expected value of the number of cars in a randomly selected household?

• 2.5

• 0.1667

• 1.45

• 1

• Cannot be determined

Tags

CCSS.HSS.MD.A.2

A dealer in Las Vegas selects 10 cards from a standard deck of 52 cards. Let Y be the number of diamonds in the 10 cards selected. Which of the following best describes this setting?

• Y has a binomial distribution with n = 10 observations and probability of success p = 0.25

• Y has a binomial distribution with n = 10 observations and probability of success p = 0.25, provided the deck is shuffled well.

• Y has a binomial distribution with n = 10 observations and probability of success p = 0.25, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected.

• Y has a geometric distribution with n = 10 observations and probability of success p = 0.25

• Y has a geometric distribution with n = 52 observations and probability of success p = 0.25.

In the town of Lakeville, the number of cell phones in a household is a random variable W with the following probability distribution (shown below).

The standard deviation of the number of cell phones in a randomly selected house is

• 1.32

• 1.7475

• 2.5

• 0.09

• 2.9575

A random variable Y has the following probability distribution (see above)

The value of the constant, C, is:

• 0.10

• 0.15

• 0.20

• 0.25

• 0.75

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

The variance of the sum of two random variables X and Y is

•  $\sigma_x+\sigma_y$  

•  $\left(\sigma_x\right)^2+\left(\sigma_y\right)^2$  

•  $\sigma_x+\sigma_y$  , but only if X and Y are independent

•  $\left(\sigma_x\right)^2+\left(\sigma_y\right)^2$  , but only if X and Y are independent

• None of these

It is known that about 90% of the widgets made by Buckley Industries meet specifications. Every hour a sample of 18 widgets is selected at random for testing and the number of widgets that meet specifications is recorded. What is the approximate mean and standard deviation of the number of widgets meeting specifications?

• $\mu=1.62\ ;\ \sigma\ =\ 1.414$

• $\mu=1.62\ ;\ \sigma\ =\ 1.265$

• $\mu=16.2\ ;\ \sigma\ =\ 1.62$

• $\mu=16.2\ ;\ \sigma\ =\ 1.273$

• $\mu=16.2\ ;\ \sigma\ =\ 4.025$

Tags

CCSS.HSS.ID.A.4

A raffle sells tickets for $10 and offers a prize of $500, $1000, or $2000. Let C be a random variable that represents the prize in the raffle drawing. The probability distribution of C is given above.

The expected profit when playing the raffle is

• $145

• $585

• $865

• $635

• $485

Let the random variable X represent the amount of money Carl Makes tutoring statistics students in the summer. Assume that X is Normal with mean $240 and standard deviation $60. The probability is approximately 0.6 that, in a randomly selected summer, Carl will make less than about

• $144

• $216

• $255

• $30

• $360

Tags

CCSS.HSS.ID.A.4

Which of the following random variables is geometric?

• The number of phone calls received in a one-hour period.

• The number of times I have to roll a six-sided die to get two 5s

• The number of digits I will read beginning at a randomly selected starting point in a table of random digits until I find a 7.

• The number of 7s in a row of 40 random digits.

• All four of the above are geometric random variables.