Question

If

npgreater than or equals≥5

and

nqgreater than or equals≥​5,

estimate

Upper P left parenthesis more than 8 right parenthesisP(more than 8)

with

nequals=1313

and

pequals=0.70.7

by using the normal distribution as an approximation to the binomial​ distribution; if

npless than<5

or

nqless than<​5,

then state that the normal approximation is not suitable.

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

Upper P left parenthesis more than 8 right parenthesisP(more than 8)equals=0.70.7

​(Round to four decimal places as​ needed.)

B.

The normal distribution cannot be used.

Answer 1

Solution:

Given:

n = 13

p = 0.7

q = 1 - p = 1 - 0.7 = 0.3

If np ≥ 5 and nq ≥ ​5, estimate

P(more than 8)=............?

n*p = 13* 0.7 = 9.1 > 5

n*q = 13 * 0.3 = 3.9 < 5

Since nq is not ≥ ​5 , we can not use Normal approximation  to the binomial​ distribution.

Thus correct answer is:

B. The normal distribution cannot be used.