The amount of orange juice in a randomly selected half-gallon container varies according to a normal distribution with a mean of 64 ounces and a standard deviation of 0.25 of an ounce.

What proportion of all containers contains less than a half-gallon (64 ounces)?

What is the median amount of orange juice in such containers?

The weight of grass seed in bags marked "50 lb" varies according to a normal distribution with a mean of 50 lb and a standard deviation of 1 ounce (0.0625 lb).

What proportion of all bags weighs less than 50 pounds?

What is the median weight of such bags?

A population of people has has a mean of 75 and a standard deviation of 12.

Random samples of size 121 are taken. Find the mean and standard deviation of the sample mean.

How would the answers to part (a) change if the size of the samples were 400, instead of 121?

Suppose the mean cost of a 30-day supply of a generic drug is $46.58, with a standard deviation of $4.84 across the country. Find the probability that the mean of a sample of 100 prices of 30-day supplies of this drug will be between $45 and $50.