Consider Youden's data on the weight of u.s. pennies given in Problem 3.10.14. Allow a 99% certainty for your answers .(a) You work for the U.S. Mint and have to move steel carts carrying 100,000 pennies. What's the maximum weight of such a cart? The steel cart itself weighs 43 pounds. (b) For a “Give a Penny ” fund-raising drive, you're weighing bags of pennies which are supposed to contain ten dollars each. Byweighing the bags you want to determine if the pennies seem to have been miscounted. If there has not been a miscount, how much should such a bag weigh? Ignore the weight of paper for rolls of pennies.Problem 3.10.14:In Chapter 5, we will introduce the idea of a “confidence interval” for an unknown parameter. It's a range of possible values for the parameter together with the probability-the “confidence coeffi-cient”-that the parameter actually falls within that range. Here, we'll look at a special case, a confidence interval for an unknown median.Suppose we've taken a sample of size n from some probability distribution (or, as a special case, from a numeric population). Call the median M and let min and max refer, respectively, to the smallest and largest observations in the sample. Then the interval (min, max) can be thought of as a range of possible values, a confidence interval, for M. In this problem, we'll determine the confidence coefficient for this interval. That is, we'll determine the probability that this interval contains the median. For simplicity, assume a random observation has a zero chance to actually equal M.(a) Identify M, min, max, and the confidence coefficient. Here's the sample:(b) Let Y be the number of observations in the sample which are less than M . What's the model for Y?(c) P(M (d) P(M > min) =? (e) What's the confidence coefficient for the interval (min, max) as a confidence interval for M?(f) What's the confidence coefficient for part (a)? (g) What's the median weight of U.S. pennies? Here are the weights W of 100 newly minted pennies, reported to the nearest 0.02 gram (taken from W.]. Youden's National Bureau of Standards Publication 672, Experimentation and Measurement):(h) In Chapter 4, we'll see that (3.11, 3.13) is a 99% confidence interval for the median weight, M, of U.S. pennies. How do you interpret this confidence interval? To what does the confidence coefficient refer? (i) What's wrong with interpreting the confidence interval in part (h) by saying “ninty-nine percent of the time, M is between 3.11 and 3.13, the rest of the time it's not”? (j) In part (g), what's the relationship between the sample median and M?