Mean of sample(help)

Independent random samples of size n1=30 and n2=50 are taken from two normal populations having the means μ1=78 and μ2=75 and the variances σ21=150 and σ22=200. Find the probability that the mean of the first sample will exceed that of the second sample by at least 4.8.

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Originally Posted by Yan

Independent random samples of size n1=30 and n2=50 are taken from two normal populations having the means μ1=78 and μ2=75 and the variances σ21=150 and σ22=200. Find the probability that the mean of the first sample will exceed that of the second sample by at least 4.8.

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Sample mean is a normally distributed random variable. And the difference of two normally distributed random variables is also a normally distributed random variable.

So find where .

Researching the details is left for you to do.