644 A survey of IQ scores of all the United States senators

6.44 A survey of IQ scores of all the United States senators in the history of the body revealed a mean of 140 and a standard deviation of 25. What ?s the probability that the average IQ score of a random sample of 16 senators a) will be lower than 120? b) will exceed 160?

Solution

(a) P(xbar<120) = P((xbar-mean)/(s/vn) <(120-140)/(25/sqrt(16)))

=P(Z<-3.2) = 0.0007 (from standard normal table)

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(b)P(xbar>160) = P(Z>(160-140)/(25/sqrt(16)))

=P(Z>3.2) = 0.0007 (from standard normal table)