In a study of facial behavior, people in a control group are timed for eye contact in a 5-minute period. Their times are normally distributed with a mean of 184.0 seconds and a standard deviation of 55.0 seconds (based on data from “Ethological Study of Facial Behavior in Nonparanoid and Paranoid Schizophrenic Patients,” by Pittman, Olk, Orr, and Singh, Psychiatry, Vol. 144, No. 1). For a randomly selected person from the control group, find the probability that the eye contact time is greater than 230.0 seconds, which is the mean for paranoid schizophrenics. Based on personal experience, does the result appear to be the proportion of people who are paranoid schizophrenics?

In use these parameters (based on Data Set 1 “Body Data” in Appendix B):

Men's heights are normally distributed with mean 68.6 in. and standard deviation 2.8 in

Women's heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in.