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STAT 400, Final Examination
Dec. 18, 1997, Thur. 10:30 - 12:30 AM
Show your work in each of the following problems.
1. (20%) Suppose the response time to a particular editing command of a computer
time-sharing system is normally distributed with standard deviation (j = Ui millisec.
( a) Construct a 90% confidence interval for the mean response time fL based on a
random sample of 25 response times with a sample average of 24.3.
(b) Calculate the sample size n to ensure that the resulting 90% C1 has a length 7.
2.(20%) Suppose the hardness of a certain alloy is normally distributed with mean
fL = 65 and standard deviation a = 4.7.
(a) A speciman is acceptable only if its harness exceeds Ei9. Compute the probability
that a randomly chosen specimen has an acceptable hardness.
(b) Derive the probability that eight or more of ten independently selected specimens
have acceptable hardness?
(Round off numberical values to the second decimal place.)
3.(20%) Let X be a random variable havin...

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