According to a recent survey conducted by Gallup.com, 20% of US adults have seen a healthcare professional for significant neck or back pain within the past year. The human resources manager of a large manufacturing company decides to investigate the issue among the company’s employees. The manager takes a random sample of 25 employees and asks them if they have seen a healthcare professional for significant neck/back pain within the past year. Assume that the rate among the company employees who visited a healthcare professional due to neck/back pain is the same as that reported by Gallup, that is, for each employee there is 20% chance that (s)he had visited healthcare professional due to neck/back pain within the past year. Employees in the company are independent of each other, that is, one employee having back/neck pain and seeking medical care does not affect the chance of other employees having neck/back pain and seeking medical care.

a. What is the probability that 8 employees in the sample say they have seen a healthcare professional for significant neck or back pain within the past year?

b. What is the probability that less than 2 employees in the sample say they have seen a healthcare professional for significant neck or back pain within the past year?

c. Compute the expected number of employees that have seen a healthcare professional for significant neck or back pain within the past year from the sample.