Question

A random sample of size n1 = 16 is selected from a normal population with a mean of 75 and variance of 288. A second random sample of size n2 = 9 is taken independently from another normal population with mean 80 and variance of 162. Let X^1 and X^2 be the two-sample means. Find the probability that X^1 + X^2 is less than 158.

Select one:

a. 0.7385

b. 0.3085

c. 0.6915

d. 0.4235

Answer 1

The given information is:

First group:

Second group:

Let and be the two sample means. Both the samples are selected from the normally distributed population. So, the addition of two sample means follows normal distribution with ; that is,

The probability that is less than 158 can be calculated as:

Using standard normal table, the P(Z<0.5) is 0.6915.

Therefore, the probability that is less than 158 is 0.6915.

Hence, the correct answer is (c).