In North America,female adult heights are approximately normalpopulation mean =6

Question

In North America,female adult heights are approximately normalpopulation mean =65 inches and population standard deviations =3.5inches.the height of 50 females were measured at a nationalvolleyball tournament.The sample mean height was found to be 70inches.

What would population parameters given above,what is theprobability of obtaining a sample mean height of 70 inches orhigher with a random sample of n=50?

Does the probability make you question the population meanstated for female heights?

Why would you believe this sample mean may not be representiveof the population of female heights?

Explanation / Answer

mean, = 65 standard deviation, = 3.5 n=50 standard error, e = / n = 3.5/50 =0.495 P(X>=70) P(Z>=(X-)/e) = P(Z>=(70-65)/0.495) =P(Z>=10.1) ˜1-1 =0 the probability calculated above obviously make mequestion the population mean stated for female heights. I believe this sample mean is not representive of thepopulation of female heights since the sample is taken from aspecific group instead of considering females diverse orheterogeneous groups in the population

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