Problem 6: (12 marks) 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.

a. (2 marks) Is it plausible that X is normally distributed?

b. (5 marks) 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. (5 marks) For a random sample of 50 such pairs, what is the (approximate) probability

that the total courtship time exceeds 150 hours?