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 (or 0.5064 using unrounded value and technology) 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.

The horizontal axis has three tick marks. In the order they appear, from the left side of the figure to the right, they are: 51,300, 51,800, and 52,300. The label 51,800 is below the maximum point on the curve and in the center of the horizontal axis.

The first area under the curve is to the left of 51,300, is shaded, and is labeled P(x

The second area under the curve is between 51,300 and 52,300, is shaded, and is labeled P(51,300 x 52,300).

The third area under the curve is to the right of 52,300 and is shaded. There is no label.

For parts (a) and (b), let the population mean be 51,800 and = 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.

x