The distribution of heights of a certain breed of terrier has a mean of 72 centi

Question

The distribution of heights of a certain breed of terrier has a mean of 72 centimeters and a standard deviation of 10 centimeters, whereas the distribution of heights of a certain breed of poodle has a mean of 28 centimeters with a standard deviation of 5 centimeters. Assuming that the sample means can be measured to any degree of accuracy, find the probability that the sample mean for a random sample of heights of 64 terriers exceeds the sample mean for a random sample of heights of 100 poodles by at most 44.2 centimeters.

Explanation / Answer

here mean differnence of height =72-28 =44

and std deviation for difference with given sample size =(102/64 +52/100)1/2 =1.3463

therefore probability that sample mean differnence is at most 44.2 =P(X<44.2)=P(Z<(44.2-44)/1.3463)

=P(Z<0.1486)=0.5590

please revert for any clarificaiton requried,

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