Question

In the EAI sampling problem, the population mean is $51,100 and the population standard deviation is $4,000. When the sample size is n = 20, there is a 0.4977 probability of obtaining a sample mean within +/- $600 of the population mean. Use z-table.

1. What is the probability that the sample mean is within $600 of the population mean if a sample of size 40 is used (to 4 decimals)?
   
   
2. What is the probability that the sample mean is within $600 of the population mean if a sample of size 80 is used (to 4 decimals)?

Answer 1

Solution:

We are given:

a. We have to find:

Using the z-score formula, we have:

Now using the standard normal table, we have:

Therefore, the probability that the sample mean is within $600 of the population mean if a sample of size 40 is used is 0.6572

b. We have to find:

Using the z-score formula, we have:

Now using the standard normal table, we have:

Therefore, the probability that the sample mean is within $600 of the population mean if a sample of size 80 is used is 0.8203