"Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. Unfortunately, the treatment also reduces the strength of the fabric. The breaking strength of untreated fabric is Normally distributed with mean 58 pounds and standard deviation 2.3 pounds. The same type of fabric after treatment has Normally distributed breaking strength with mean 30 pounds and standard deviation 1.6 pounds.4 A clothing manufacturer tests an SRS of 5 specimens of each fabric.
(a) What is the probability that the mean breaking strength of the 5 untreated specimens exceeds 50 pounds?
(b) What is the probability that the mean breaking strength of the 5 treated specimens exceeds 50 pounds?