Statistics Unit Review

At a large high school 40 percent of the students walk to school, 32 percent of the students have been late to school at least once, and 37.5 percent of the students who walk to school have been late to school at least once. One student from the school will be selected at random. What is the probability that the student selected will be one who both walks to school and has been late to school at least once?

• 0.12

• 0.15

• 0.1875

• 0.345

• 0.72

The table shows the probability distribution for the prize amounts that will be awarded at a school raffle.

Let the random variable P represent a randomly selected prize amount. What is the expected value of P?

• $1.00

• $3.90

• $4.00

• $10.00

• $17.20

At a large university, data were collected on the number of sisters and brothers that each student had. Let the random variable X represent the number of sisters and the random variable Y represent the number of brothers. The distribution of X has mean 1.00 and standard deviation 0.94. The distribution of Y has mean 1.07 and standard deviation 1.04. What is the mean of the distribution of X+Y?

• 1.98

• 2.01

• 2.04

• 2.0528

• 2.07

Julio sells computers at an electronics store. Let the random variable C represent the number of computers that Julio sells in one week. The table shows the probability distribution of C. Julio earns $800 per week, with a commission of $200 per computer sold. What is the expected value of Julio’s earnings for one week?

• $3.31

• $662

• $1,462

• $2,848

• $3,310

Parker has a part-time job picking apples. Let the random variable A represent the number of baskets of apples picked each day. The distribution of A has mean 4.5 baskets and standard deviation 1.3 baskets. Parker is paid $65 per day plus $5 per basket. What are the mean μ and standard deviation σ of Parker’s daily pay?

• μ=$87.50 and σ=$71.50

• μ=$87.50 and σ=$6.50

• μ=$22.50 and σ=$6.50

• μ=$87.50 and σ=$1.30

• μ=$22.50 and σ=$71.50

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?

• 0.10

• 0.28

• 0.47

• 0.53

• 0.76

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?

• 0.24

• 4.11

• 4.24

• 16.79

• 16.92

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?

• 8.17

• 28.3

• 66.7

• 73.4

• 94.4

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 15 independent trials

• A binomial variable with 25 independent trials

• A variable that is not binomial with 25 independent trials

• A binomial variable with 40 independent trials

• A variable that is not binomial with 40 independent trials

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

• 0.0921

• 0.4780

• 0.5220

• 0.5563