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# Normal and Random Probability distributions

1. customers in a bank
A bank has a drive thru service. The number of customers arriving during a 15 minute period is distributed as shown.
Find the mean, variance, and standard deviation for the distribution

Number of customers X 0 1 2 3 4

Probability P(X) 0.30 0.50 0.10 0.08 0.02

The number of inquiries received per day for a college catalog is distributed as shown.
Find the mean, variance, and standard deviation for the data

Number of inquiries X 22 23 24 25 26 27

Probability P(X) 0.08 0.19 0.36 0.25 0.07 0.05

3. Drug dizziness
If 10% of the people who are given a certain drug experience dizziness, find the probabilities for a sample of 15 people who take the drug
At least 2 people will become dizzy
exactly 3 people will become dizzy
at most 4 people will become dizzy

4. salaries for actuaries
The average salary for graduates entering the actuarial field is \$40,000. If the salaries are normally distributed with a standard deviation of
\$5,000, find the probability that
An individual graduate will have a salary over \$45,000.
A group of nine graduates will have a group average over \$45,000.

5. Suitcase weights
The average weight of an airline passenger's suitcase is 45 pounds. The standard deviation is 2 pounds.
If 15% of the suitcases are overweight, find the maximum weight allowed by the airline. Assume the variable is normally distributed.