Homework Sourse651 A survey of the IQ scores of all the United States senat
6.51 A survey of the IQ scores of all the United States senators in the history of this body revealed a mean of Mu=140 and a standard deviation of Sigma =25. What is the probability that the average IQ score of a random sample of 16 senators (a) will be lower than 120? (b) will exceed 160? (c) will be between 85 and 115. 
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)
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(c) P(85<xbar<115) = P((85-140)/(25/sqrt(16)) <Z< (115-140)/(25/sqrt(16)))
=P(-8.8<Z<-4) = 0 (from standard normal table)
