The Diversity, Equity, and Inclusion (DEI) office of a major multinational bank is investigating the process used to make recent hires for financial analysts. The office knows that exactly 10% of all applications were from minority candidates and that exactly 9% of the open positions were filled by members of a minority
For the investigation, the DEI office will take a random sample of 900 applications. Let p-hat be the proportion of minority applicants in the sample.
Answer the following

Find the mean of p-hat

Find the standard deviation of p-hat

Compute an approximation for P(p-hat less than or equal to 0.09) which is the probability that there will be fewer minority applicants in the sample than were hired by the bank. Round your answer to four decimal places