A machine fills boxes of fish fingers to a mean volume of 368 grams with a standard deviation of 15 grams. Assume that the volumes in the bottles are normally distributed. If a sample of 25 boxes is randomly selected:
a. What is the probability that the sample mean will be below 368g?
b. What is the probability that the sample mean will be below 360 grams?
c. What is the probability that the sample mean will be between 360 grams and 370 grams?
d. Now assume that we did not know the population mean amount in the boxes and all we know is that the amount of fish finders in individual boxes are normally distributed. Now you select a random sample of 25 boxes and find that the sample mean is 365 grams and the sample standard deviation is 10 grams. Set up a 95% confidence interval for population mean.
e. Using the same information as part (d) above, now find the 99% confidence interval for population mean.
f. Why is the second interval larger than the first?