Company X is a manufacturer that manufactures cans of tuna that are advertised with a net weight of 6 ounces. ABC Auditors is reviewing inventory for Company X. During interim field work, Company X has informed ABC Auditors that the net weight is a normal random variable with a mean of 6.05 ounces and a standard deviation of .18 ounces. While conducting its materiality threshold, ABC Auditors has determined that as long as the mean weight is not less than 5.97 ounces, inventory is not materially understated. In order to test whether inventory is not less than the 5.97 ounces as determined by the calculated materiality threshold, ABC Auditors selected a random sample of 36 cans for further investigation.

1) Calculate the probability that the mean weight of the sample is less than 5.97 ounces.

2) Suppose the random sample of 36 cans of tuna produced a mean weight that is less than 5.97 ounces. Comment on the statement made by the manufacturer.

Please show all steps involved in solving.