A kitchen gadget has the diagonal approximately normally distributed, with a mean of 2.56 inches and a standard deviation of 0.04 inch. Suppose you select a random sample of 9 kitchen gadgets,

a)Find the sampling distribution of the mean

b)What is the probability that the sample mean is less than 2.54 inches?

c)What is the probability that the sample mean is between 2.55 and 2.57 inches?

d)The probability is 70% that the sample mean will be between what two values symmetrically distributed around the population mean?

Present answer with 5 decimals.