Use a normal approximation to find the probability of the in

Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 109 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 27 voted. WORK NEEDS TO BE SHOWN.

Thank you!

Solution

mean = 109 * 0.22 = 23.98

std dev = sqrt (109 * 0.22 * 0.78) = 4.32

P(X < 27) = P(Z < (27 - 23.98) / 4.32 )

                = P(Z < 0.7)

                = 0.7580