Samples of size 60 are drawn from a large population known to have a mean of 78 and a standard deviation of 12. What proportion of these samples would we expect to have a mean greater than 80?
Α. .098
B. .902
C. 566
D. Almost none
Ε. .434
The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size. In this case, the standard error of the mean would be 12 / √60 ≈ 1.55.
To find the proportion of samples with a mean greater than 80, we need to find the z-score for a mean of 80.
z = (80 - 78) / 1.55 = 1.29
Using a standard normal distribution table or calculator, we find that the proportion of samples with a mean greater than 80 is approximately 0.098, which corresponds to answer choice:
A. .098