Question

6.  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.

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

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

c. The time between two successive arrivals to a bank

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

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

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

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

h. 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 dead-line, and your bonus is $0 if the project is completed after the deadline

i. 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 1P 2 502 dollars if the price P a month from now is greater than $50

Answer 1

ou - The of among row on 9 the SARAS virus betweens 1.se ARS he adjustment in the dow mechanical nomla "ong now and in a months time can be Communi. ed a fostvettved negative-ve) doci by the industrial nalmal can be increment of lessening with time along there lines industrial name can be communicated as folas binomial aud If the change is to be detumined over huge amount of infomation that is number of Preliminaris o binomial distribution incik then it very sensible to expect the typical distrubution as the simihlicy to binomial

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ci here it isnt sensible to expect that the distrubution of the time between two sicousive appearances to a bank follows oldinaly diserubution this is just the care of exponentia distrubution as its intredes at appealence time.

d) The distrubutions of the time taken by the bank employee to suppole an albiraly client can be thought to be oldinaly,

o the length of the fun of the mill drive on a standard by Phill-michallson can be sensibly accepted to a typical distrubution