Find the mean and standard deviation of the following binomial distributions:
For n = 8 trials, compute the probability that r > 1 for each of the following values of p:
Harley Davidson, director of quality control for the Kyoto Motor company is conducting his monthly spot check of automatic transmissions. In this procedure, 10 transmissions are removed from the pool of components and are checked for manufacturing defects. Historically, only 2 percent of the transmissions have such flaws. (Assume that flaws occur independently in different transmissions.)
- What is the probability that Harley's sample contains more than two transmissions with manufacturing flaws?
- What is the probability that none of the selected transmissions has any manufacturing flaws?
Diane Bruns is the mayor of a large city Lately, she become concerned about the possibility that large numbers of people who are drawing unemployment checks are secretly employed. Her assistants estimate that 40 percent of unemployment beneficiaries fall into this category, but Ms.Bruns is not convinced. She asks one of here aides to conduct a quiet investigation of 10 randomly selected unemployment beneficiaries.
- If the mayor's assistants are correct, what is the probability that more than eight of the individual investigated haver jobs? (Do not use the tables.)
- If the mayor's assistants are correct, what is the probability that only three of the investigated individuals have jobs? (Do not use the tables.)
A month later, Mayor Bruns picks up the morning edition of the city's leading newspaper, the sun-American, and reads an expose of unemployment fraud.
A recent study of how American spend their leisure time surveyed workers employed more than 5 yuears. They determined the probability an employee has 2 weeks of vacation time to be 0.45, 1 week of vacation time to be 0.10, and 3 or more weeks to be 0.20. Suppose 20 workers are selected at random. Answer the following questions without Appendix Table 3.
- What is the probability that 8 have 2 weeks of vacation time?
- What is the probability that only one worker has 1 week of vacation time?
- What is the probability that at most 2 of the workers have 3 or more weeks of vacation time?
- What is the probability that at least 2 workers have 1 week of vacation time?
Harry Ohme is in charge of the electronics section of a large department store. He has noticed that the probability that a customer who is just browsing will buy something is 0.3. Suppose that 15 customers browse in the electronics section each hour. Use Appendix Table 3 in the back of the book to answer the following questions:
- What is the probability that at least one browsing customer will buy something during a specified hour?
- What is the probability that at least four browsing customers will buy something during a specified hour?
- What is the probability that no browsing customers will buy anything during a specified hour?
- What is the probability that no more than four browsing customers will buy something during a specified hour?
Given a binomial distribution with n = 28 trials and p = 0.025, use the poisson approximation to the binomial to find.
Given a binomial distribution with n = 30 trials and p = 0.04, use the poisson approximation to the binomial to find.