normal approximation to find probability

Question

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

108

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

30

voted

The probability that fewer than

30

of

108

eligible voters voted is ***blank***

​(Round to four decimal places as​ needed.)

Answer 1

n = 108, p = 0.22

mean = np = 23.76

standard deviation = sqrt(npq) = 4.3

x = score

z = (x - mean)/standard deviation

P(x < 30) = P(z < (30 - 23.76)/4.3) = P(z < 1.45)

P(z < 1.45) = 0.9265