please i need help with this one

please don't use excel or google sheet use an actual equation

8.2.9) A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected, and the diameter is measured. The resulting data (in millimeters) are as follows: 8.20 8.25 8.18 8.25 8.22 8.20 8.28 8.28 8.18 8.24 8.25 8.25 8.17 8.26 8.22 (a) Check the assumption of normality for rod diameter. (b) Calculate a 99% two-sided confidence interval on mean rod diameter. (c) Calculate a 99% upper confidence bound on the mean. (d) Compare this bound with upper bound of the two-sided confidence interval and discuss why they are different.8.6.3) Consider the suspension rod diameter measurements described in Exercise 8.2.9 (use the modified data of 8.2.9 as given in Chapter 8 homework problems), Compute a 99% prediction interval on the diameter of the next rod tested. Compare the length of the prediction interval with the length of the 99% CI on the population mean. 8.6.8) Consider the suspension rod diameter data in Exercise 8.2.9 (use the modified data of 8.2.9 as given in Chapter 8 homework problems). Compute a 99% tolerance interval on the diameter of the rods described that has 95% confidence. Compare the length of the tolerance interval with the length of the 99% CI on the population mean. Which interval is shorter? Discuss the difference in the interpretation of these two intervals