Let X denote the courtship time for a randomly selected female-male pair of mating scorpion flies (time from the beginning of interaction until mating). Suppose the mean value of X is 120 min and the standard deviation of X is 110 min (suggested by data in the article "Should I Stay or Should I Go? Condition- and Status-Dependent Courtship Decisions in the Scorpion Fly Panorpa Cognate" (Animal Behavior, 2009: 491-497)).
a. Is it plausible that X is normally distributed?
b. For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 100 min and 125 min?
c. For a random sample of 50 such pairs, what is the (approximate) probability that the total courtship time exceeds 150 hr?
d. Could the probability requested in (b) be calculated from the given information if the sample size were 15 rather than 50? Explain.