In: Statistics and Probability
Suppose we are interested in the Annual Salary of Electronics Associated, Inc. (EAI) managers and we find that for a sample of
n = 30
managers, there was 0.5034 probability of obtaining a sample mean within ± $500 of the population mean (see the figure below).
The title of the diagram is "Sampling Distribution of x". A bell-shaped curve divided into three areas is above a horizontal axis labeled x. The text = 730.30 is on the figure.
For parts (a) and (b), let the sample mean be 51,800 and σ = 4,000. (Round your answers to four decimal places.)
(a)
What is the probability that
x
is within ±$500 of the population mean if a sample of size 50 is used?
(b)
Answer part (a) for a sample of size 100.