Question

Consider the probability that more than 39 out of 149 houses for lose power once a year. Assume the probability that a given house will lose power once a year is 2%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

Answer 1

To determine whether the normal curve can be used as an approximation to the binomial probability in this scenario, we need to verify the necessary conditions:

1. The number of trials, n, is sufficiently large.

2. The probability of success, p, is not extremely close to 0 or 1.

Let's check these conditions:

1. The number of trials, n, is 149, which is reasonably large.

2. The probability of success, p, is given as 2%. To check if p is not extremely close to 0 or 1, we can calculate np and n(1 - p) and check if both values are greater than or equal to 5.

np = 149 * 0.02 = 2.98

n(1 - p) = 149 * (1 - 0.02) = 146.02

Since both np and n(1 - p) are greater than or equal to 5, the condition is satisfied.

Therefore, both conditions necessary for using the normal curve as an approximation to the binomial probability are satisfied in this case.

We can approximate the binomial probability of more than 39 houses losing power once a year using the normal distribution.