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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.

#### Solution Summary

There are 5 problems related to probabilty disrtibutions. First two deal with finding mean,standard deviation and variation for given probability distributions. Other two problems are involves finding probabilities for normal and binomial probability distributions. Last problem is finding the limit of weight that a passenger can carry in aeroplanes.

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