A pediatrician's records showed the mean height of a random sample of 36 girls at age of 1 year to be 29.530 inches with a standard deviation of 1.0953 inches. Assuming that this was a random sample, construct a 95 percent confidence interval for the population mean height of girls of 1 year.

a) Show that the necessary conditions needed for the inference about population mean stated by the central limit theorem are satisfied/met. b) Construct a 95 percent confidence interval for the mean height of girls of 1 year. Show your work. Report the lower and upper bounds of the confidence interval, and round these limits to 4 decimal points. c) Provide the interpretation of the confidence interval you obtained in b) Problem 4 (1 point). a) Consider the information provided in Problem 3. What sample size n would be needed to construct a 95% confidence interval for the population mean height with the margin of error or 0.20 inches? b) If you assume that the margin of error of the confidence interval is 0.20 inches, then what can you tell about the range of this confidence interval, i.e., what is the value of the range of the C.I. (in inches)? c) What sample size n would be needed to construct a 99% confidence interval for the population mean height with the margin of error or 0.20 inches? d) Compare the values of sample size n in a) and c). Which one is larger? why?