was stats CLT problem for previous parts

do only q5 c and 5e

step by step with full workout

Write formula when necessary really clearly

Question 5 To investigate the actual contents of 600ml bottles of drinking water marketed by a well- known Australian company, a Market Research Team took a randomly selected sample of 36 water bottles of the same brand. The sample mean and standard deviation of the random sample were found to be 598mL and 4.9mL respectively. Assume that the distribution of the content of water in the bottles is normal with mean 600mL and standard deviation 3.5mL. (a) What type of distribution will the sampling distribution of the sample mean be? State its parameters and the values of those parameters in this context. ( b ) Find the probability that the mean of the random sample will exceed 601mL. (C If the population mean and standard deviation were unknown, what would be the 95% confidence interval for the population mean of content of the bottles? (d) Find the probability that the sample mean of a random sample of size 50 from the population will exceed 601ml. (e) mark.) If the Market Research Team wants to halve the margin of error, how many times larger or smaller should the sample size (n) be