# Finding probabilities associated with a commercial loan officers approval statistics.

A commercial loan officer at a local bank estimates that she approves 10% of all small business loans for which her customers apply. Suppose 20 customers apply for small business loans this week.

a. What is the expected number of loans that will be approved?

b. Find the standard deviation of the number of loans approved.

c. Find the probability that she will approve at least ten (10) loans.

d. Find the probability that she will approve less than five (5) loans.

e. The shape of the distribution used in this problem is (skewed, symmetric).

f. The variable in this problem is (discrete, continuous).

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#### Solution Summary

Given an initial approval % and a sample of 20 customers, the problem demonstrates the processes of calculating various statistics such as mean, standard deviation, probability of approval, and skewness.