Interpersonal violence (e.g., rape) generally leads to psychological stress for the victim. Clinical Psychology Review (Vol. 15, 1995) reported on the results of all recently published studies of the relationship between interpersonal violence and psychological stress. The distribution of the time elapsed between the violent incident and the initial sign of stress has a mean of 5.1 years and a standard deviation of 6.1 years. Consider a random sample of n = 150 victims of interpersonal violence. Let x-bar represent the mean time elapsed between the violent act and the first sign of stress for the sampled victims.
a. Give the mean and standard deviation of the sampling distribution of x-bar.
b. Will the sampling distribution of x be approximately normal? Explain.
c. Find P(x-bar > 5.5).
d. Find P(4 < x-bar < 5).