Statistics probability

Question

Use a normal approximation to find the probability of the indicated number of voters. In this​ case, assume that 144 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 37 voted

Answer 1

for normal approximation: mean = np = 144 * 0.22 = 31.68 and standard deviation = sqrt(npq) = sqrt(144*0.22*0.78) = 4.97

compute z = (x - mean)/SD for x = 37, mean = 31.68 and SD = 4.97.

z = (37 - 31.68)/4.97 = 1.07

find P(z < 1.07) from standard normal probability table = 0.8577