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

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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.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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