Name: ______Date: ______

Statistics & ProbabilityMs. Parent

Sampling Distributions about the Mean Review

  1. What is a sampling distribution? Describe its center, spread, and shape in general in comparison to a population distribution.
  1. Assume the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 100 women are randomly selected, find the probability that this sample has a mean height less than 64 inches. Show your work and interpret your answer.
  1. The Wechsler Adult Intelligence Scale (WAIS) is a common “IQ test” for adults. The distribution of WAIS scores for persons over 16 years of age is approximately Normal with a mean of 100 and a standard deviation of 15.
  2. What is the probability that a randomly chosen individual has a WAIS score of 105 or higher? Show your work and interpret your answer.
  1. What is the probability that the average WAIS score of a random sample of 60 people is 105 or higher? Show your work and interpret your answer.
  1. Is part a. or part b. more likely? Why?
  1. A delivery company’s trucks occasionally get parking tickets, and based on past experience, the company plans that the trucks will average 1.3 tickets a month, with a standard deviation of .7 tickets.
  2. If they have 18 trucks, what is the probability that the company will get fewer than 12 tickets? Assume a normal model.
  1. If a random sample of 8 trucks is selected, what is the probability that the company will have an average of greater than 1 ticket per truck? Assume a normal model.
  1. You work for Consumer Reports and are sent to the Goodyear factory to test their claim that the life span of their new model of tires is on average 50,000 miles with a standard deviation of 800 miles. You select 64 tires at random ant test them. The mean lifespan of this sample comes out to be 49,721 miles.
  2. What were the chances of the mean of this sample coming out to 49,721 miles or less?
  1. In your report, what would you say about Goodyear’s claim that their tires have an average life span of 50,000 miles?
  1. A particular high school boasts that its students have unusually high GPA’s. A random sample of 80 students from this school was selected, and the mean GPA was 3.2. If the mean GPA of all students is known to be 3.0 with a standard deviation of .05, is the high school justified in its claim? Explain.