Math 370X - Quiz 10Saumil PadhyaNovember 14, 2016Name Net ID1.Let X and Y be the number of hours that a randomly selected person watches movies andsporting events, respectively, during a three-month period. The following information isknown about X and Y:E(X) = 50, E(Y ) = 20, V ar(X) = 50, V ar(Y ) = 30, Cov(X, Y ) = 10.The totals of hours that different individuals watch movies and sporting events during the threemonths are mutually independent.One hundred people are randomly selected and observed for these three months. Let T be thetotal number of hours that these one hundred people watch movies or sporting events during thisthree-month period.Approximate the value of P[T < 7100].(A) 0.62(B) 0.84(C) 0.87(D) 0.92(E) 0.972.An insurance company issues 1250 vision care insurance policies. The number of claims filedby a policyholder under a vision care insurance policy during one year is a Poisson randomvariable with mean 2. Assume the numbers of claims filed by different policyholders aremutually independent.Calculate the approximate probability that there is a total of between 2450 and 2600 claimsduring a one-year period?(A) 0.68(B) 0.82(C) 0.87(D) 0.95(E) 1.0013.An investor invests 100 dollars in a stock. Each month, the investment has probability 0.5 ofincreasing by 1.10 dollars and probability 0.5 of decreasing by 0.90 dollars. The changes inprice in different months are mutually independent.Calculate the probability that the investment has a value greater than 91 dollars at the end ofmonth 100.(A) 0.63(B) 0.75(C) 0.82(D) 0.94(E) 0.974.A company provides a death benefit of 50,000 for each of its 1000 employees. There is a1.4% chance that any one employee will die next year, independent of all other employees.The company establishes a fund such that the probability is at least 0.99 that the fund willcover next year’s death benefits.Calculate, using the Central Limit Theorem, the smallest amount of money, rounded to thenearest 50 thousand, that the company must put into the fund.(A) 750,000(B) 850,000(C) 1,050,000(D) 1,150,000(E)
View Full Document
Unlocking...