Question

e. Suppose a random sample of size 100 is taken from a distribution with mean 200 and variance 400. What is the distribution of the sample mean ?%? (State the name and parameter(s) of the distribution)

f. For a medical test, the probability of testing positive for a healthy person is 5%. Based on this, can we find the probability of testing positive for an infected person? If yes, explain how; if no, explain why.

Answer 1

e. As the sample size is greater than 30, we use the normal distribution as the sample mean distribution. The mean of the sample mean will be the same as the mean of the sample, while the variance of the sample mean will be the variance of the sample divided by the sample size.

Given:

we will have:

So, the distribution of the sample mean will be:

f. The testing positive of a healthy person is a false positive. Whereas the testing positive of an infected person is a true positive. There is no relation between the probability of false positive cases and the probability of true positive cases. A good test will have a high probability of true positives as well as a low probability of false positives. At the same time, a bad test can have a high probability of true positives and a high probability of false positives.

As there is no relation, we cannot find the probability of testing positive for an infected person from the probability of testing positive for a healthy person.