Question

USING EXCEL:

Consider the probability that no fewer than 75 out of 111 houses will lose power once a year. Assume the probability that a given house will lose power once a year is 98%

Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

PLEASE USE EXCEL AND SHOW EXCEL FORMULAS USED FOR SOLUTION. THANK YOU!!

Answer 1

Solution:

Given:

n = sample size = Number of houses = 111

p = probability that a given house will lose power once a year = 98% = 0.98

X = Number of houses will lose power once a year follows a binomial distribution with parameters n = 111 and p = 0.98

We have to check if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

The necessary conditions are :

and

Thus we get:

Since second condition is not satisfied , we can not use the normal curve as an approximation to the binomial probability.

Thus we need to use Binomial probability to find the probability.

We have to find:

P( No fewer than 75 out of 111 houses will lose power once a year ) = ........?

That is:

P( 75 or more houses out of 111 houses will lose power once a year ) =.........?

That is:

We need to use Excel command:

=1-BINOM.DIST(x , trials , probability , cumulative)

=1 - BINOM.DIST(74, 111, 0.98, TRUE)

=1

Thus required answer is:

the probability that no fewer than 75 out of 111 houses will lose power once a year is 1.