From the meticulously compiled annual report on medicalstatistics in the U.S., a

Question

From the meticulously compiled annual report on medicalstatistics in the U.S., a typical adult male has an averagecholesterol reading of 242.2 mg/dL with a standard deviation of45.4 mg/dL. If you randomly select 25 adult males what is theprobability that the average cholesterol reading of your samplegroup will be greater than 253 mg/dL? From the meticulously compiled annual report on medicalstatistics in the U.S., a typical adult male has an averagecholesterol reading of 242.2 mg/dL with a standard deviation of45.4 mg/dL. If you randomly select 25 adult males what is theprobability that the average cholesterol reading of your samplegroup will be greater than 253 mg/dL?

Explanation / Answer

Let X be the cholesterol reading. We are given=242.2 and =45.4 for the population. For a sampleof n=25 we have by the central limit theorem that Xbar is normalwith =242.2 andxbar=/25=45.4/5=9.08. Therefore, for Z=(Xbar-)/(/n) P(Xbar>253)=1-P(Z<(253-242.3)/9.08)=1-P(Z<-1.17841)=1-.88=.12

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