Question

In the EAI sampling problem, the population mean is $71,900 and the population standard deviation is $5000. For n = 30, there is a 0.4908 probability of obtaining a sample mean within +$600 of the population mean.

a. What is the probability that I is within $600 of the population mean if a sample of size 60 is used (to 4 decimals)?

Answer 1

To find the probability that the sample mean is within $600 of the population mean when a sample of size 60 is used, divide the population standard deviation by the square root of the sample size and calculate the Z-score using the given difference.

Then, use a standard normal distribution table or calculator to find the probability associated with the Z-score.

Step-by-step explanation:

To find the probability that the sample mean is within $600 of the population mean when a sample of size 60 is used, we can use the standard deviation of the population divided by the square root of the sample size.

Given that the population standard deviation is $5000 and the sample size is 60, we can calculate the standard error of the mean as follows:
Standard Error of the Mean (SEM) = Population Standard Deviation / √(Sample Size) = $5000 / √(60)

Then, we can use the Z-score formula to find the probability:
Z-score = (Sample Mean - Population Mean) / SEM = $600 / SEM

Using a standard normal distribution table or calculator, we can find the probability associated with the Z-score, which will give us the probability that the sample mean is within $600 of the population mean.