In an effort to reduce health care costs, many companies are encouraging their employees to walk more. According to the Medicine & Science in Sports & Exercise Journal, Americans take an average of 5,117 steps per day. Assume the population standard deviation is 2,200 steps per day. Jim Powers is the manager of a retail store that employs 230 people and has provided each of them with a pedometer which counts the number of steps taken per day. He chooses a random sample of 45 employees and records the number of steps they walked yesterday. Assume the employee population is representative of the U. S. population.

a. What is the probability that the sample mean is less than 5,800 steps per day?

b. What is the probability that the sample mean is more than 4,800 steps per day?

c. What is the probability that the sample mean is between 4,600 and 5,000 steps per day?