Suppose a random sample of n = 25 observations is selected from a population tha

Question

Suppose a random sample of n = 25 observations is selected from a population that is normally distributed with mean equal to 103 and standard deviation equal to 13.(

a) Give the mean and the standard deviation of the sampling distribution of the sample mean x.

(Enter your standard deviation to two decimal places.)

(b) Find the probability that x exceeds 108. (Round your answer to four decimal places.)

(c) Find the probability that the sample mean deviates from the population mean = 103 by no more than 3. (Round your answer to four decimal places.)

Explanation / Answer

A. Sample mean will be 103 and sample standard deviation will be 13/sqrt(25) or 13/5 or 2.6

B. P(x>108)= P(z>(108-103)/5) =P(z>1) or 1-P(z<1) = 1-0.8413 or 0.1587 ( from normal distribution table)

C. P(100<xbar<106) = P((100-103)/(5/sqrt25)<z<(106-103)/(5/sqrt(25)) = P(-3<z<3) or 2*P(z<3)-1 . From normal distribution table. 2*0.9987-1 or 0.9974

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