a.A random sample of size 81 is taken from a large population, measuring the time it takes to complete driver's license examination.The sample mean was found to be 43 minutes, and the sample standard deviation 5.71 minutes.Construct a 95% confidence interval around the sample mean. Be sure to show whether you use the t- or z- value, and what value you use. Interpret the confidence interval in a single sentence. In another sentence, state why you used either the "t" or the "z".

b.Determine the necessary sample size for a confidence interval around a sample mean:Set the confidence level at 95%; the population standard deviation, even though unknown, is estimated to be 6.5 (in the same units of measure as the sample mean), and the desired margin of error is 1.5.What sample size would you need to use to accomplish this result?Please show how you computed this.