answer the following include step by step how to do in excel and a write up to answer each question. C.1. For each of the following uncertain quantities, discuss whether it is reasonable to assume that the probability distribution of the quantity is normal. If the answer isn't obvious, discuss how you could discover whether a normal distribution is reasonable.

The change in the Dow Jones Industrial Average between now and a year from now

The length of time (in hours) a battery that is in continuous use lasts

The time between two successive arrivals to a bank

The time it takes a bank teller to service a random customer

The length (in yards) of a typical drive on a par 5 by Phil Michelson

The amount of snowfall (in inches) in a typical winter in Minneapolis

The average height (in inches) of all boys in a randomly selected seventh-grade middle school class

Your bonus from finishing a project, where your bonus is $1000 per day under the deadline if the project is completed before the deadline, your bonus is $500 if the project is completed right on the deadline, and your bonus is $0 if the project is completed after the deadline

Your gain on a call option on a stock, where you gain nothing if the price of the stock a month from now is less than or equal to $50 and you gain (P-50) dollars if the price P a month from now is greater than $50

C.2. For each of the following uncertain quantities, discuss whether it is reasonable to assume that the probability distribution of the quantity is binomial. If you think it is, what are the parameters n and p? If you think it isn't, explain your reasoning.

The number of wins the Boston Red Sox baseball team has next year in its 81 home games

The number of free throws Kobe Bryant misses in his next 250 attempts

The number of free throws it takes Kobe Bryant to achieve 100 successes

The number out of 1000 randomly selected customers in a supermarket who have a bill of at least $150

The number of trading days in a typical year where Microsoft's stock price increases

The number of spades you get in a 13-card hand from a well-shuffled 52-card deck

The number of adjacent 15-minute segments during a typical Friday where at least 10 customers enter a McDonald's restaurant

The number of pages in a 500 sheet book with at least one misprint on the page

C.3. The Poisson distribution is often appropriate in the "binomial" situation of n independent and identical trials, where each trial has probability p of success, but n is very large and p is very small. In this case, the Poisson distribution is relevant for the number of successes, and its parameter (its mean) is np. Discuss some situations where such a Poisson model might be appropriate. How would you measure n and p, or would you measure only their product np? Here is one to get you started: the number of traffic accidents at a particular intersection in a given year.

C.4. One disadvantage of a normal distribution is that there is always some probability that a quantity is negative, even when this makes no sense for the uncertain quantity. For example, the time a light bulb lasts cannot be negative. In any particular situation, how would you decide whether you could ignore this disadvantage for all practical purposes?