A fishing line manufacturer claims that his new X-25 series has an average tensile strength (µ) of 25 psi. To verify his claim, a sample of 25 specimens was tested and yielded the following results:

32, 19, 27, 24, 28, 29, 38, 30, 25, 33, 18, 25, 37, 28, 20, 32, 23, 21, 25, 19, 23, 27, 32, 26, 30

a. N the sample data following a normal distribution? If the specification is 25 ± 5 psi, what's the percentage of this fishing line not meeting the specifications?
b. Based on the 90% confidence interval for p, is the manufacturer's claim valid? Flow large a sample is needed if we wish to be 90% confident that our sample mean will be within 1 psi of the true mean?