A company manufactures doorknobs, and the mean width should be 3.8cm. Each day, a random sample of 5 doorknobs is taken and the width is measured. Assume the population has a normal distribution. Here is a random sample of the width of 5 doorknobs: 3.92 3.83 3.78 3.81 3.88 a) use a calculator, spreadsheet, or stat crunch to calculate the mean and standard deviation of the sample. b) compute the 99% confidence intervals. Show all the steps, including the formulas and the calculations. c) explain your answer in part (b) in the context of this situation. d) Based on your interval, would you conclude that the population mean of doorknobs is greater than 3.8 cm? Why or why not