Please answer the following question and show work! Answer all parts. Thank you **7.82 Gestation Periods of Humans.**For humans, gestation periods are normally distributed with a mean of 266 days and a standard deviation of 16 days.**a.** Use the technology of your choice to simulate 2000 samples of nine human gestation periods each.**b.** Find the sample mean of each of the 2000 samples.**c.** Obtain the mean, the standard deviation, and a histogram of the 2000 sample means.**d.** Theoretically, what are the mean, standard deviation, and distribution of all possible sample means for samples of size 9?**e.** Compare your results from parts (c) and (d).

Please check the answer explained belowStep 1 Hello there, I have used excel to generate the Random no of 2000 sample of size 9 each. It is not possible to show all the data here. Here, I am providing the procedure how to generate the random no using excel and also shown few data here. Steps to generate random no in excel Go to data => Data analysis => Select Random no generation=>Enter the following details in the box as shown below=> click ok Statistics homework question answer, step 1, image 1 fullscreenExpand Step 2 The data generated is shown below. It is shown upto 26 samples here Statistics homework question answer, step 2, image 1 fullscreenExpand Step 3 b) Use the following formula to get the sample mean “=average(A1:A9)” drag this to the right till the 2000th sample to get the sample mean of each of the sample Screenshot of few samples is shown here Statistics homework question answer, step 3, image 1 fullscreenExpand Step 4 c) Use the following formula to get the standard deviation “=STDEV.S(A1:A9)” drag this to the right till the 2000th sample to get the sample standard deviation of each of the sample. Screenshot of few sample is shown here Statistics homework question answer, step 4, image 1 fullscreenExpand Step 5 Steps to generate Histogram of each sample is shown below Select the row, by clicking on 10th row, Go to insert => click on insert statistic chart => select histogram from that Histogram plotted is shown below Statistics homework question answer, step 5, image 1 fullscreenExpand Step 6 d) Mean = 266 (Using formula =”AVERAGE(A1:BXX9)”) Standard deviation = 16 (Using formula =”STD.P(A1:BXX9)”) From the histogram, distribution is normal distribution e) The mean and sample standard deviation of each sample is varying but it is close to 266 and 16. The overall mean = 266 and standard deviation = 16