98年國立臺北大學金融與合作經營學系統計學線上測驗

1.: The number of telephone calls that arrive at a phone exchange is assumed on the
average 12 calls per hour. What is the probability there are exactly 5 calls in 30 minutes?
(1)

2.: If X and Y are independent, normal random variables with E(X ) = 5 , E(Y) = 10 ,
Var(X ) = 4 , Var(Y) = 9 . Find Var(2X + 3Y − 2) = ? (2) ;
P(2X + 3Y < 40) = ? (3)

3.: We know that the standard deviation of burning rate of the rocket propellant is σ = 2 .
Suppose we want the error in estimating the mean burning rate to less than 0.5cm/ s ,
with 95% confidence. Find the required sample size? (4) ?

4.

5.: In a random sample of 100 automobile engine crankshaft bearing, 12 have a surface
finish that is rougher than the specification allow. Construct a 95% two-sided
confidence interval for the proportion of bearings in the population. (9)

6.

7.: A local bank reviewed its credit card policy with the intention of recalling some of its
credit cards. In the past approximately 5% of cardholders defaulted, leaving the bank
unable to collect the outstanding balance. The bank also found that the probability of
missing a monthly payment is 0.20 for customers who do not default. Of course, the
probability of missing a monthly payment for those who default is 1.
(一) What is the prior probability that the customer will default? (11)
(二) Given that a customer missed one or more monthly payments, compute the
posterior probability that the customer will default? (12)

8.

StreetInsider.com reported 2007 earnings per share data for a sample of major
companies (February 12, 2008). Prior to 2007, financial analysts predicted the 2007
earnings per share for these same companies. Use the following data to test for any
differences between the population mean actual and population mean estimated
earnings per share.

9.

(一) Compute the test statistic.       (16)
(二) Compute the p -value.      (17)
(三) Give your conclusion for this test.        (18)

10.

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