2. A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years): 2.0 1.3 6.0 1.9 5.1 0.4 1.0 5.3 15.7 .7 4.8 0.9 12.2 5.3 0.6 a. Assume that the lifetime distribution is exponential and use an argument parallel to that of Example 7.5 to obtain a 95% confidence interval for expected (true average) lifetime. b. How should the interval of part (a) be altered to achieve a confidence level of 99%? c. What is a 95% confidence interval for the standard deviation of the lifetime distribution? Hint: What is the standard deviation of an exponential random variable