Could you please provide step-by-step explanation for the answers of the following questions

15 The average age of doctors in a certain hospital is 50 0 years old . Suppose the distribution of ages is normal and has a standard deviation of 60 years . If 9 doctors are chosen at random for a committee , find the probability that the average age of those doctors is less than 50.6 years . Assume that the variable is normally distributed Ans : 61 8 %16 . A sample of 35 different payroll departments found that employees worked an average of 240 .5 days a year . If the population standard deviation is 18 8 days a ) find the point estimate of the population mean Ans : Point estimate : 240 6 days b / find the 90% confidence interval for the average number of days a worked by all employees who are paid through payroll departments Ans : 235 . 4 45 245.8 17 . Four squirrels were found to have an average weight of 9 0 ounces with a sample standard deviation is a 7 Find the 95% confidence interval of the true mean weight Ans: 79 cul 18 . A study of elephants is conducted to determine the average weight of a certain subspecies a elephants . The standard deviation for the population is 500 pounds . At a 95% level , how many elephants need to be weighed so the average weight will be accurate to within 200 pounds ? Ans : 25