Independent random samples of sizes n1 = 30 and n2 = 50 are taken from two

normal populations having the means 1 = 78 and 2 = 75 and the variances

2

1 = 150 and

2

2 = 200. Use the distribution of difference of two sample means,

to calculate the probability that the mean of the first sample will exceed that of

the second sample by at least 4.8.