數學問題~ 請進 help1

a) Normal distribution.
mean=32, sd=12
b) n=35
P(X_bar > 28) = P(Z > (28-32)/(12/√(35)))
= P(Z > -1.97) = 0.9756
c) P(X_bar > T) = 0.15
P(Z > (T-32)/(12/√(35))) = 0.15
(T-32)/(12/√(35)) = 1.035
T-32 = 2.099
T = 34.10 (cor. to 2 d.p.)

數學問題~ 請進 help1
According to past records, the average project completion time for a specific type of project of a construction company is 32 weeks with a standard deviation of 12 weeks. A random sample of 35 projects of similar type was selected from the record of the company:

a) What type of distribution will the sample mean project completion time follow and what is the mean and standard deviation of this distribution? Explain briefly.

b) What is the probability that the sample mean project completion time will be greater than 28 weeks?

c) After doing some analysis with the sample, the project manager wants to set up a time T (in a week) as the deadline for all future similar type of projects. If it is expected that the probability that the sample mean project completion time will exceed time T is 15%, find the value of T. Keep the accuracy of your answer to two decimal places.
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