# Mean of sample(help)

• March 8th 2009, 06:47 PM
Yan
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.
• March 8th 2009, 10:13 PM
mr fantastic
Quote:

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.

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 $\Pr(Y > 4.8)$ where $Y = \overline{X}_1 - \overline{X}_2$.

Researching the details is left for you to do.