The amount of water in a bottle is approximately normally distributed with a mean of

2.75

liters with a standard deviation of

0.035

liter. Complete parts (a) through (c) below.

a. If a sample of 4 bottles is selected, what is the probability that the sample mean amount contained is less than 2.72 liters?

b. If a sample of 25 bottles is selected, what is the probability that the sample mean amount contained is less than 2.72 liters?

c. Explain the difference in the results of (a) and (b).

The sample size in (c) is greater than the sample size in (b), so the standard error of the mean (or the standard deviation of the sampling distribution) in (c) is

less

or

greater

than in (b). As the standard error

increases,

or

decreases,

values become more concentrated around the mean. Therefore, the probability that the sample mean will fall close to the population mean will always

increase

or

decrease

when the sample size increases.