Suppose interpersonal violence generally leads to psychological stress for a victim. According to reported results, the distribution of the time elapsed between the violent incident and the initial sign of stress is approximately normal with a mean of 5.1 years and a standard deviation of 6.1 years.

a)What is the probability that a randomly selected victim exhibits the first sign of stress between 4.5 and 5.5 years after interpersonal violence?

b)Consider a random sample of 150 victims of interpersonal violence and let the sample mean represent the mean time elapsed between the violent act and the first sign of stress for the sampled victims. What is the probability that the sample mean elapsed time is between 4.5 and 5.5 years?

c) Compare the probabilities a) and b). Which one is bigger? Explain why you expect one to be bigger than the other.