Ch. 6 Random Variables

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

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.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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

Which of the following probability distributions of a discrete random variable X is a legitimate probability distribution?

• 
• 
• 

Let Z = the number students in Mr. Rooney’s English class who arrive late on a randomly selected day. The expected value of Z is 2. Which one of the following is the best interpretation of what this means?

• We can be confident that at least 2 students will be late to Mr. Rooney’s class on a randomly selected day.

• On average, the number of students who are late to Mr. Rooney’s class on a randomly selected day is 2.

• There are 2 students in Mr. Rooney’s class who almost always arrive late.

The weight of a medium-sized orange selected at random from a large bin of oranges at a local supermarket is a random variable with mean μ = 12 ounces and standard deviation σ = 1.2 ounces. Suppose we independently select two oranges at random from the bin. The difference in the weights of the two oranges (the weight of the first orange minus the weight of the second orange) is a random variable with a standard deviation equal to

• 0 ounces.

• 1.70 ounces.

• 2.88 ounces.

In a certain large population, 70% are right-handed. You need a left-handed pitcher for your softball team and decide to find one by asking people chosen from the population at random. (We assume that once you do find a left-hander, he or she will be happy to join your team and will say yes.) Which of the following is closest to the probability that you will have to ask four or more people before finding your first left-hander?

• 0.103

• 0.147

• 0.343

Tags

CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

counts the number of successes in a fix number of trails. X = 0,1,2,3,…,n

• Geometric

• Binomial

• Both

• Neither

counts the number of trials needed to obtain the 1st success. X = 1,2,3,…

• Geometric

• Binomial

• Both

• Neither