Question

Use a normal approximation to find the probability of the indicated number of voters. In this​ case, assume that 144eligible 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 34 voted

The probability that fewer than 34 of 144 eligible voters voted is?

Answer 1

Result:

Use a normal approximation to find the probability of the indicated number of voters. In this​ case, assume that 144eligible 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 34 voted

The probability that fewer than 34 of 144 eligible voters voted is?

n=144 and p=0.22

Expectation = np = 31.68

Variance = np(1 - p) = 24.7104

Standard deviation = 4.9710

Using normal approximation with continuity correction, z value for 34,

Z = (33.5-31.68)/4.9710 =0.37

P( x < 34) = P( z < 0.37)

=0.6443

Excel function to get probability: =NORM.S.DIST(0.37,TRUE)