Download Statistics Exam 2 - Probability and Confidence Intervals and more Exams Probability and Statistics in PDF only on Docsity! STAT 100 Exam 2 A April 8, 1996 Directions: Work each problem, showing all steps in your solution. You may use calculators. Do not spend too much time on any one problem. 1.) (a) For a standard normal random variable Z, find: (i) (5pts) P[IZI>2.7]. (ii) (5 pts) z so that P[ Z > z ] = 0.8849 . (b) For a normal random variable X with mean 5 and standard deviation 2, find: (i) (5 pts) P[X<6]. (ii) (5 pts) b so that P[ 3 < X < b ] = 0.6826 . 2.) For a certain type of lightbulb the probability of burning out after 6 months of constant use is 0.3. A random sample of 100 of those lightbulbs is taken. (a) (10 pts) What is the approximate probability that at least 30 lightbulbs are burned out after 6 month of constant use? (b) (10 pts) What is the approximate probability that after 6 months at least 70 bulbs are not burned out? 3.) The distribution of salary of persons working in a large city has H = $28,000 and a = $4,000 . Two hundred persons are randomly sampled. (a) (10 pts) What can you say about the distribution of the sample mean? (b) (10 pts) What is the approximate probability that X exceeds $29,000? 4.) An accounting firm wishes to determine the average time |i required for employees to complete a certain audit operation. Times from 180 employees yield a sample mean of 4.1 hours and a sample standard deviation of 1.6 hours. Construct a 95% confidence interval for the population mean \JL . (20 pts) 5.) Suppose that it was found that of those smokers who wish to quit 70% still smoke 1 year later. A psychologist claims that a 1 year hypnotic therapy seems to help people to stop smoking. The psychologist wishes to provide strong evidence that this claim correct. (a) (4 pts) Let p be the probability a person smokes after the hypnotic treatment. What are the null and alternative hypotheses for this claim in terms of p? (b) (6 pts) To test his claim the psychologist gave a group of 19 smokers his hypnotic therapy. Let X be the number of these who still smoke after the therapy. Write a rejection region in terms of X with level of significance a = 0.10. (c) (5 pts) Suppose 8 people still smoked after the treatment what would you conclude from your test? (d) (5 pts) What is the P-value of a sample with 8 remaining smokers?
