The graph at the right show the
frequency distribution of a population with a population mean of 2.5 and a population standard
deviation of 3.

If samples of size 25 (n =25) were taken from the population which
graph would most likely be a good representation of the distribution of the sample means?

Use the central limit theorem if
possible. For a sample of n = 36, find the probability of a sample mean being
greater than 43 given and .
The population is also normally distributed.

(Hint: First determine and and use those values to find )

Use the central limit theorem if
possible. For a sample of n = 9, find the probability of a sample mean being less than
7 given and . The population is
not normally distributed.

a.

0.1587

c.

0.8413

b.

0.3694

d.

Cannot be determined because the sample size is
too small.

At a restaurant near the high
school, the restaurant manager has determined that each customer on average spends $9.10 ( ) with a standard deviation of $3.00 (). The customer data was
normally distributed.

A group of 4 friends (n = 4) went to the restaurant
together and one of the friends bought lunch for entire group. What is the probability that the total
bill will be more than $40? (Hint: This suggests finding the
probability that the sample mean would be greater than $10.00.)

The length of pregnancies are
normally distributed with a mean of 268 days ( ) and a standard
deviation of 15 days ().

A group of 36 pregnant women
(n = 36) were in a parenting class together. What is the probability that
the average pregnancy for the women lasted longer than 270 days?