Chapter 4, Problem 4.189ACI

Whistle-blowing among federal employees. Whistle-blowing refers to an employee's reporting of wrongdoing by co-workers. A survey found that about 5% of employees contacted had reported wrongdoing during the past 12 months. Assume that a sample of 25 employees in one agency are contacted and let x be the number who have observed and reported wrongdoing in the past 12 months. Assume that the probability of whistle-blowing is .05 for any federal employee over the past 12 months.

1. a. Find the mean and standard deviation of x. Can x be equal to its expected value? Explain.
2. b. Write the event that at least 5 of the employees are whistle-blowers in terms of x. Find the probability of the event.
3. c. If 5 of the 25 contacted have been whistle-blowers over the past 12 months, what would you conclude about the applicability of the 5% assumption to this agency? Use your answer to part b to justify your conclusion.