Shown are the ages of the presidents at the times of their deaths. my questions are A-E **Educational Resource: Statistical Analysis on Presidential Ages****Data Set:**The following represents the ages (in years) of the Presidents at the time of their deaths:- 66, 67, 68, 67, 90- 88, 60, 63, 71, 83- 78, 72, 70, 53, 65- 46, 64, 67, 49, 73- 64, 81, 57, 57, 74- 93, 60, 71, 64, 80- 93, 90, 67, 77, 78- 93, 63, 71, 56, 79**Instructions:**Please show all your work. You can upload a PDF file or Word document file. Answer only submissions are not acceptable.**Questions:**a) Do the data represent a population or a sample?b) Select a random sample of 15 ages and find the variance and standard deviation.c) Find the 98% confidence interval of the standard deviation.d) Find the standard deviation of all the data values.e) Does the confidence interval calculated in part c contain the standard deviation?**Notes:**- When selecting the random sample, ensure that the selection process is unbiased.- Use appropriate statistical formulas for variance and standard deviation.- Confidence intervals should be calculated using standard statistical methods for sampling distributions.

A population is an entire group that you want to draw conclusions about. A sample is a specific group that you will collect data from. The size of the sample is always less than the total size of the population. Furthermore, a population is always greater than 30 units.Hence, the given data set is a populationThe table of 15 random numbers was produced according to the following specifications: Numbers were randomly selected from within the range of 46 to 93. Duplicate numbers were not allowed from a random number table 66, 56, 86, 81, 82, 80, 85, 71, 77, 84, 51, 76, 75, 90, 83 For ease of calculations, we construct the following table: 66 56 86 81 82 80 85 71 77 84 51 76 75 90 83 Variance 122.7429 S.D. 11.07894 Mean 76.2 We will use the sample mean square formula defined for a sample selected from a population to determine the sampling variance. The Excel- formulae used are as follows: Variance =VARA(array)=122.7429 Standard deviation =STDEV(array)=11.07894 Mean =Average(array)=76.2(c) Since you have posted a question with multiple subparts, we will solve the first 3 subparts for you. To get the remaining subpart done please repost the -–- question and mention the subparts to be solved.