A firm engaged in manufacturing undergarments for gents employs 100 male and 144

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 probabilityCase
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.