Suppose a simple random sample of size n 64 is obtained fro

Suppose a simple random sample of size n = 64 is obtained from a population with mu = 73 and sigma = 32. (a) Describe the sampling distribution of x-bar. (b) What is P (x-bar > 79)? (c) What is P [x

Solution

(a)B

mean = 73

standard deviation =s/vn =32/sqrt(64)=4

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(b)P(xbar>79) = P((xbar-mean)/(s/vn) >(79-73)/(32/sqrt(64)))

=P(Z>1.5) =0.0668 (from standard normal table)

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(c)P(xbar<=64) =P(Z<(64-73)/(32/sqrt(64)))

=P(Z<-2.25) =0.0122 (from standard normal table)

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(d)P(68.8<xbar<81.4) = P((68.8-73)/(32/sqrt(64))<Z<(81.4-73)/(32/sqrt(64)))

=P(-1.05<Z<2.1) =0.8353 (from standard normal table)