Calculating Probabilities for Sampling Distribution — Quiz Answers

A fair six-sided number cube is rolled 60 times. What is the probability that fewer than 10 percent of the rolls are a five? Use the z -table.

A coin is bent so that, when tossed, "heads” appears two-thirds of the time. What is the probability that more than 70 percent of 100 tosses result in "heads”? Use the z -table.

Driving instructors Mr. Adams and Mr. Bateman teach class independently of each other. Among Mr. Adams’s students, 68 percent pass the driving test on the first try, while 74 percent of Mr. Bateman’s students pass the driving test on the first try. Suppose there are 40 students in Mr. Adams’s class and 50 students in Mr. Bateman’s class. Let cap A is equal to the proportion of students who pass the driving test on the first try from Mr. Adams’s class and cap b is equal to the proportion of students who pass the driving test on the first try from Mr. Bateman’s class. What is the probability that Mr. Bateman’s class has more students who pass on the first try? Use the z -table.

In a large urban high school, 68 percent of the students take public transportation to and from school. Annette takes a random sample of 75 students from this school. What is the probability that more than 70 percent of the students in the sample take public transportation to and from school? Use the z -table.

In a certain town, 62 percent of the residents enjoy riding roller coasters. Alfred takes a sample of 75 residents from this town. What is the probability that fewer than 58 percent of the residents in the sample enjoy riding roller coasters? Use the z -table.

In a beach town, 13 percent of the residents own boats. A random sample of 100 residents was selected. What is the probability that less than 11 percent of the residents in the sample own boats? Use the z -table.

On any given day, 34 percent of sales at Ruby’s jewelry store are from necklaces, while 28 percent of sales at Nugget Jewels are from necklaces. Suppose Ruby’s has 50 customers and Nugget Jewels has 60 customers on a randomly selected day. Let cap r is equal to the proportion of sales that are from necklaces at Ruby’s and cap n is equal to the proportion of sales that are from necklaces at Nugget Jewels. What is the probability that the proportion of sales from necklaces at Ruby’s will be less than the proportion of sales from necklaces at Nugget Jewels? Use the z -table.

Ricardo and Tammy practice putting golf balls. Ricardo makes 47 percent of his putts and Tammy makes 51 percent of her putts. Suppose that Ricardo attempts 25 putts and Tammy attempts 30 putts. Let cap r is equal to the proportion of putts Ricardo makes and cap t is equal to the proportion of putts Tammy makes. What is the probability that Ricardo makes a higher proportion of putts than Tammy? Use the z -table.

A fair six-sided number cube has the following faces: 1 , 1 , 2 , 2 , 5 , 6 This number cube is rolled 50 times. What is the probability that fewer than 30 percent of the rolls result in a two? Use the z -table.

At a certain high school, 38 percent of freshmen and 31 percent of sophomores walk to school. Suppose that random samples of 40 freshmen and 45 sophomores are chosen. Let cap s is equal to the proportion of sophomores who walk to school and cap f is equal to the proportion of freshmen who walk to school. What is the probability that the proportion of sophomores who walk to school is greater than the proportion of freshmen? Use the z -table.