Question

Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.

n=6060, p=0.20.2, X=25

Can the normal distribution be used to approximate this probability?

A. Yes, the normal distribution can be used because np(1−p) ≥ 10.

B. No, the normal distribution cannot be used because np(1−p) < 10.

C. No, the normal distribution cannot be used because np(1−p) ≥ 10.

D. Yes, the normal distribution can be used because np(1−p) < 10.

Approximate P(X) using the normal distribution. Select the correct choice below and fill in any answer boxes in your choice.

A. P(X) =

(Round to four decimal places as needed.)

B. The normal distribution cannot be used.

By how much do the exact and approximated probabilities differ? Select the correct choice below and fill in any answer boxes in your choice.

A. ___

(Round to four decimal places as needed.)

B. The normal distribution cannot be used.

Answer #1

We are given n = 60 , p = 0.2 so q = 1- p = 1-0.2 =0.8

The normal distribution can be used if np(1−p) ≥ 10.

np(1−p) = 60*0.2*0.8 = 9.6 < 10

**B. No, the normal distribution cannot be used because
np(1−p) < 10.**

P(X) = ??

**B. The normal distribution cannot be used. so we can not
find P(x) using normal approximation.**

By how much do the exact and approximated probabilities differ? Select the correct choice below and fill in any answer boxes in your choice.

Since we can not use normal approximation ,we can not find the difference in the probability .

**B. The normal distribution cannot be used.**

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