Question

Use a normal approximation to find the probability of the indicated number of voters. In this case assume that 150 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.

The probability that fewer than 39 of 150 eligible voters voted is

Answer 1

The number of people who voted follows a binomial distribution with probability of having voted
`p=0.22` and
`n=150` subjects, which means the approximating normal distribution should have mean
`np=33` and standard deviation
`√(np(1-p))\approx5.07`.

With the continuity correction, you have


`\mathbb P(X<39)\approx\mathbb P(X<38.5)=\mathbb P\left((X-33)/(5.07)<(38.5-33)/(5.07)\right)=\mathbb P(Z<1.08)\approx0.86`