After post-graduate study, Mike found a job as HR analyst in London. The company iscurrently recruiting Chief Marketing Officer. The HR department recently sent out aknowledge test to the applicants after the initial CV screening. At this stage of selection, thecompanydoesnotinvitethelowestscoring20%backforthenextface-to-face interview.

According to the historical data, the test scores on this test are normally distributed and has a meanof75withstandarddeviationof15.

a What mark (to the nearest whole number) must a candidate achieve to secure aninterview?

(3 marks)

b. Howmuch isthe 95%confidenceintervalforthetestscores if the sample size is 90 applicants?

(7 marks)

c. The company offers free buffet lunch for candidates attending the interview.As aHR analyst, Mike is asked to estimate the amount of salad to order for the interviewday. Sampling suggests that the amount of salad taken by each candidate distributes as the below diagram. What is the distribution as described and probability densityfunction of the distribution in the diagram? What is the probability of the blue areainthediagram?