Question 1:

The foreman of the canning division of the Acme Peanuts company observed that the amount of cashews in a "48 ounce" can varies from can to can. Records indicate that the process follows a normal probability distribution with a mean of 48.6 ounces and a standard deviation of 0.35 ounces.

a) The foreman randomly selects 25 cans from the canning line and determines that the mean amount of cashews per can is 48.4 ounces. Compute the probability that a sample of 25 cans would have a mean greater than or equal to 48.4 ounces.

b) Compute the probability that a sample of 16 cans would have a mean greater than or equal to 48.75 ounces.

Question 2:

Captain Tuna is sold in cans that have a net weight of 8 ounces. The weights are normally distributed with a mean of 8.025 ounces and a standard deviation of 0.135 ounces. You take a sample of 36 cans. Compute the probability that the sample would have a mean:

a) greater than 8.05 ounces?

b) less than 7.995 ounces?