Moira works as the loan officer at a bank. Every day he needs to manage numerous loan applications by verifying each document provided by the applicants, which correspond with the bank’s policy. At the same time, she essentially distributes the approved loans into three categories based on the applicants’ ability to repay per month. She allocated the approved applicants who are able to repay about $2,000 per month to category 1;

$5,000 per month to category 2; and $10,000 per month to category 3. She recorded the number of loan applications with the respective probability of approval for the past four days in the following table:

Daily Number of Loans Probability of Approval 111 0.20 125 0.32 103 0.25 136 0.23 For the four days, Moira discovered that about 45% of approved applications belong to category 1, 35% belong to category 2, and the remaining belong to category 3.

a. Compute the expected number of approved loans for each category.

b. Find the standard deviation of approved loans for all four days.

c. Based on your findings in part

b, justify whether the calculation can be used to determine the standard deviation values for each category.