Problem 5 (20 points, 5 each) Past experience and factory tests show that the lifetime for a car battery is normally distributed with mean 148 weeks and standard deviation 8 weeks. a. What percentage of the car batteries would have life length between 136 and 160 weeks? b. If a grade A battery lasts for 170 weeks, can we say that this battery belongs to the top 1% in terms of lifetime? Explain. c. Suppose the manufacturer company wants to offer a guarantee with this product. If the company is willing to replace the worst 5% in terms of lifetime, how long a guarantee period should be offered? 8 d. Suppose you would like to verify your answer to Part cusing R. Choose the appropriate R function and fill-in the blanks correctly to get the answer. Choose and fill one function only! dnorm mean = sd = log = pnorm mean = lower.tail log.p = anorm ( mean = sd = lower.tail = log.p = __) mean = sd