A random sample of size 64 is taken from a normal population having a mean of 75

Question

A random sample of size 64 is taken from a normal population having a mean of 75 and a standard deviation of 5. A second random sample of size 36 is taken from a different normal population having a mean of 60 and a standard deviation of 2. Find the probability that the sample mean computed from the 64 measurements will exceed the sample mean computed from the 36 measurements by at least 14.2 but less than 15.4. Assume the difference of the means to be measured to the nearest tenth. f the standard normal distribution table normal distribution tabl The probability is Round to four decimal places as needed.)

Explanation / Answer

here expected mean difference =75-60=15

and std error of mean difference =(52/64+22/36)1/2 =0.7083

hence P(14.2<X<15.4)=P((14.2-15)/0.7083<Z<(15.4-15)/0.7083)=P(-1.13<Z<0.56)=0.7123-0.1292=0.5831

( please try 0.5830 if this comes wrong and revert)

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