statistic using a normal probability

Question

Use a normal approximation to find the probability of the indicated number of voters. In this​ case, assume that

164164 eligible voters aged​ 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged​ 18-24, 22% of them voted.

Probability that fewer than 42

voted

The probability that fewer than

42

of

164

eligible voters voted is ?

Answer 1

The mean of this approximate normal distribution is (22%) * (164 people) = 36.08 people

The standard deviation is √(n*p*q) = √(164 * 22% * 78%) = 5.31 people

using normcdf(-999999, 42, 36.08, 5.31) on a TI-84 or TI-83, we get an answer of 86.75%