AP Stat Unit 4 Progress Check: MCQ Part C

According to a 2018 survey, 74 percent of employed young adults expect to bring work on a vacation trip. A random sample of 20 employed young adults will be selected. What is the probability that 8 of the selected young adults will expect to bring work on a vacation trip?

(20/8)(0.74)^8(0.26)^12

Past records indicate that 15 percent of the flights for a certain airline are delayed. Suppose flights are randomly selected one at a time from all flights. Assume each selection is independent of another. Which of the following is closest to the probability that it will take 5 selections to find one flight that is delayed?

0.0783

A representative from a company that manufactures items for left-handed people will attend a large convention. The representative hopes to find a left-handed person at the convention to try out the items. The representative will select an attendee at random until a left-handed person is found. Assume each selection is independent of another. If 10 percent of the convention attendees are left-handed, what is the probability that the representative must select 4 attendees to find one who is left-handed?

0.1(0.9^3)

Approximately 9 percent of the residents of a large city have seen a certain theater production that is currently playing in the city. A marketing researcher will randomly select residents until one is found who has seen the production. What is the expected number of residents the researcher will need to ask to find someone who has seen the production?

11.11

The random variable K has a geometric distribution with mean 16. Which of the following is closest to the standard deviation of random variable K ?

15.49

According to a 2016 survey, 6 percent of workers arrive to work between 6:45 A.M. and 7:00 A.M. Suppose 300 workers will be selected at random from all workers in 2016. Let the random variable W represent the number of workers in the sample who arrive to work between 6:45 A.M. and 7:00 A.M. Assuming the arrival times of workers are independent, which of the following is closest to the standard deviation of W ?

4.11

In the United States, the generation of people born between 1946 and 1964 are known as baby boomers, and the generation of people born between 1981 and 1996 are known as millennials. Currently, 18 percent of the population are baby boomers and 27 percent of the population are millennials. A random sample of 500 people will be selected. Let the random variable B represent the number of baby boomers in the sample, and let the random variable M represent the number of millennials in the sample. By how much will the mean of M exceed the mean of B ?

45

According to a 2015 Census Bureau survey, 75,511 of the 822,959 residents of Baltimore County, Maryland, were enrolled in college. Consider a sample of 800 residents of Baltimore County, Maryland in 2015 selected at random. Which of the following is closest to the expected value of the number in the sample enrolled in college?

73.4

A random sample of n people selected from a large population will be asked whether they have read a novel in the past year. Let the random variable R represent the number of people from the sample who answer yes. The variance of random variable R is 6. Assume the responses are independent of each other. If the proportion of people from the population who read a novel in the past year is 0.40, which of the following is the best interpretation of random variable R ?

A binomial variable with 25 independent trials

During a severe storm, electrical transformers that function independently are expected to operate 85 percent of the time. Suppose 20 electrical transformers are randomly selected from the population. Let the random variable T represent the number of electrical transformers operating during a severe storm. Which of the following is the best interpretation of the random variable T ?

It is a binomial variable with mean 17 transformers and standard deviation 2.55√2.55 transformers.

At a certain restaurant, 35 percent of the customers order the daily special each day. Assume that each day the customers arrive randomly and order independently. Let the random variable X represent the number of orders placed until the first daily special is ordered. The distribution of X is geometric and has an expected value of approximately 2.86. Which of the following is the best interpretation of the expected value?

Over many days, it takes about 2.86 orders, on average, to be placed until the first daily special is ordered.

In a certain region, 10 percent of the homes have solar panels. A city official is investigating energy consumption for homes within the region. Each week, the city official selects a random sample of homes from the region. Let random variable Y represent the number of homes selected at random from the region until a home that has solar panels is selected. The random variable Y has a geometric distribution with a mean of 10. Which of the following is the best interpretation of the mean?

Over many weeks, it takes 10 homes, on average, before a home with solar panels is selected.

A local department store estimates that 10 percent of its customers return the merchandise they purchase. Let the random variable R represent the number of returns for a random sample of 40 customers. Assume that random variable R follows a binomial distribution. What is described by the value of (40/8)(0.1)^8(0.9)^32?

The probability that 8 customers in the sample will return merchandise

A thumbtack that is tossed can land point up or point down. The probability of a tack landing point up is 0.2. A simulation was conducted in which a trial consisted of tossing 5 thumbtacks and recording the number of thumbtacks that land point up. Many trials of the simulation were conducted and the results are shown in the histogram. Based on the results of the simulation, which of the following is closest to the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed?

0.28

In the United States, 75 percent of adults wear glasses or contact lenses. A random sample of 10 adults in the United States will be selected. Which of the following is closest to the probability that fewer than 8 of the selected adults wear glasses or contact lenses?

0.47