Answer to Question #100942 in Statistics and Probability for David Shuman

Question

(c) Suppose n = 50 and p = 0.19. (For each answer, enter a number. Use 2 decimal places.)
n·p =
9.50

Correct: Your answer is correct.

n·q =
40.50

Correct: Your answer is correct.


Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank
Yes
No
Correct: Your answer is correct.
second blank
can
cannot
Correct: Your answer is correct.
third blank
n·q exceeds
n·p exceeds
n·q does not exceed
both n·p and n·q exceed
n·p and n·q do not exceed
n·p does not exceed
Correct: Your answer is correct.
fourth blank (Enter an exact number.)


What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.)
μp̂ = mu sub p hat =


σp̂ = sigma sub p hat =

Answer 1

(c) Suppose n = 50 and p = 0.19.

$$n\cdot p=50\cdot 0.19=9.50$$ $$n\cdot p=9.50$$

$$n\cdot q=50\cdot (1-0.19)=40.50$$ $$n\cdot q=40.50$$

Can we approximate p̂ by a normal distribution? Why?

Yes, p̂ can be approximated by a normal random variable because both n·p and n·q exceed 5.

What are the values of μp̂ and σp̂?

$\mu_ {\hat{p}}=np=9.500$

$\sigma_ {\hat{p}}=\sqrt{npq}=2.774$