Question

Consider the probability that no fewer than 74 out of 112 houses will lose power once a year. Assume the probability that a given house will lose power once a year is 97%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

Answer 1

Answer: the normal curve can be used as an approximation to the binomial probability considering the following condition: when the sample is large, in this case n=112

Explanation:

for a binomial experiment to be approximated to normal distribution, the following conditions must be present:

i. sample size must be large, in this case sample size is 112

ii. the mean must be equal to np,where n is sample size and p is probability of success

iii. the standard deviation must be equal to npq,where q is the probability of failure