​​​ The aptitude test scores of applicants to a university graduate program are normally distributed with mean 500 and standard deviation 60.a) Applicants need a test score higher than 530 to be admitted into the graduate program. What proportion of applications qualify?[Marks 2]b) If the university wishes to set the cutoff score for graduate admission so that only the top 10% of applicants qualify for admission, what is the required cutoff score?[Marks 2]c) What percentage of applicants have test scores within two standard deviations of the mean?[Marks 3]Question 2Government officials in Canberra have recently expressed concern regarding overruns on military contracts. These unplanned expenditures have been costing Australians millions of dollars every year. The prime minister impanels a committee of experts to estimate the average amount each contract costs the government over and above the amount agreed upon. The committee has already determined that the standard deviation in overruns is $17.5 million, and that they appear normally distributed.i. If a sample of 25 contracts is selected, how likely is it the sample will overestimate the population mean by more than $10 million?[Marks 3]ii. The prime minister will accept an error of $5 million in the estimate of µ. How likely is he to receive an estimate from the committee within the specified range?[Marks 4]