A health agency is taking a survey regarding the evaluation of all the hospitals inMelbourne to find out the statistical calculation and analyze the attributes of thedata. The agency needs a report that can analyze the number of admissions, typeof control and type of service and other factors. They focus on the serviceprovided by each hospital whether it is for non-government, non-federal, forprofit, federal government and so on.For analytical purposes a random sample of 60 data is generated out of 300population data and the statistical summary of the sample data is tabulated inTable 1.Your overall task is to investigate the effect of various variables on the number ofadmissions in Melbourne hospitals using various descriptive analyses which isextremely helpful to formulate a conclusion.To assist with your investigation, you are required to answer questions 1 and 2below.Table 1 Statistical SummaryVariable Mean Median StandarddeviationMinimum Maximum Range P value CountAdmissions 6959.00 4636.50 6995.56 441.00 37375.00 2668.50 0.168 60P a g e 3 | 5Question 1 [15 marks]a) For a series of random samples of 60, are the mean values of these randomsamples normally distributed? Explain[3 marks]b) Calculate the standard error of the mean and explain the meaning of thisvalue.[2 marks]c) Determine the 95% confidence interval and explain its meaning in thecontext of the overall problem.[4 marks]d) What is the probability that a sample of 60 hospitals selected at random inthe Melbourne area will have a mean greater than 7000.00 admissions?[4 marks]e) If the admissions times were more variable, what effect would this have onthe confidence interval?[2 marks]