Question

If

npgreater than or equals≥5

and

nqgreater than or equals≥​5,

estimate

Upper P left parenthesis more than 7 right parenthesisP(more than 7)

with

nequals=1111

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.

Answer 1

SOLUTION:

From given data,

np ≥​5   estimate  Upper P left parenthesis more than 7 right parenthesisP(more than 7)

with n=11 and   p=0.70

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

np <5  or nq<​5,  then state that the normal approximation is not suitable.

Where ,

n=1111

p=0.70

Upper P left parenthesis more than 7 right parenthesisP(more than 7)

Sampling distribution can be approximated by normal if both np and nq are 5 or more , lets calculate.

np = 11* 0.70

= 7.7

Since np<5, that is  

now ,

nq = n(1-p)

= 11(1-0.70)

= 11(0.3)

= 3.3

where ,  np<5 that is 3.3<5

The conditions for normal approximation are not satisfied .

We can not proceed with further calculations.

and

The normal distribution cannot be used.