It has been reported that the average U.S. office worker receives 14 fax messages per day. For purposes of this exercise, we will assume that the daily number of fax messages is normally distributed with a standard deviation of 5.0 messages.
For an office in which 10 workers are employed, and considering these persons as a simple random sample of all U.S. office workers, what is the probability that the office will receive at least 160 fax messages (i.e., a sample mean of at least 16 faxes per worker) next Wednesday?