A firm engaged in manufacturing undergarments for gents employs 100 male and 144 female workers. The average production per day of a male worker is 60 items with a variance of 15 items, and that of a female workers is 65 items with a variance of 12 items. Find the probability

Case Question:

That a sample of 40 females gives an average production which is more than that based on a sample of 36 males by more than 6 items, assuming sampling with replacement, and that, the sample size for the two sexes being the same, the average production of females is more than that of males by less than 6 items, assuming sampling without replacement.