"Durable press" cotton fabrics are treated to improve theirrecovery from wrinkles after washing. Unfortunately, the treatmentalso reduces the strength of the fabric. The breaking strength ofuntreated fabric is normally distributed with mean 52.5 pounds andstandard deviation 2.4 pounds. The same type of fabric aftertreatment has normally distributed breaking strength with mean 29.9pounds and standard deviation 1.6 pounds. A clothing manufacturertests 5 specimens of each fabric. All 10 strength measurements areindependent. (Round your answers to four decimal places.) (a) Whatis the probability that the mean breaking strength of the 5untreated specimens exceeds 50 pounds? (b) What is the probabilitythat the mean breaking strength of the 5 untreated specimens is atleast 25 pounds greater than the mean strength of the 5 treatedspecimens?
