A sample of size100is selected from a population with

p=0.40.

(a)What is the expected value of

p?

(b)What is the standard error of

p?

(Round your answer to four decimal places.)

(c)Show the sampling distribution of

p.

A bell-shaped curve is above a horizontal axis labeledp.

• The horizontal axis ranges from about -0.10 to about 0.20.
• The curve enters the viewing window near -0.10 just above the horizontal axis and curves up to the right and reaches a maximum near 0.05.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 0.20.

A bell-shaped curve is above a horizontal axis labeledp.

• The horizontal axis ranges from about -2.60 to about 3.40.
• The curve enters the viewing window near -2.60 just above the horizontal axis and curves up to the right and reaches a maximum near 0.40.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 3.40.

A bell-shaped curve is above a horizontal axis labeledp.

• The horizontal axis ranges from about -0.15 to about 0.15.
• The curve enters the viewing window near -0.15 just above the horizontal axis and curves up to the right and reaches a maximum near 0.00.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 0.15.

A bell-shaped curve is above a horizontal axis labeledp.

• The horizontal axis ranges from about 0.25 to about 0.55.
• The curve enters the viewing window near 0.25 just above the horizontal axis and curves up to the right and reaches a maximum near 0.40.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 0.55.

(d)What does the sampling distribution of

p

show?

a. The probability distribution ofpis approximately normal with a mean of 0.40.

b. The probability distribution ofpis approximately normal with a mean of 0.05.

c. The probability distribution ofpis approximately normal with a mean of 0.

d. The probability distribution ofpis approximately normal with a mean of 100.