The breaking strength (in kg/mmm) for a certain type of fabric has mean 1.86 and standard deviation 0.27. (a) What is the probability that the sample mean breaking strength of a random sample of 100 pieces of fabric is less than 1 .8 kg/mm?
(b) What is the probability that the sample mean breaking strength of a random sample of 36 pieces of fabric is less than 1 .8 kg/mm?
(c) How large a sample size is needed so that the probability is 0.01 that the sample mean is less than 1.8?