Question

Use a normal approximation to find the probability of the indicated number of voters. In this​ case, assume that 120 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 exactly 32 voted

Answer: The probability that exactly 32 of 120 eligible voters voted is

Answer 1

Solution :

Given that,

p = 22% = 0.22

q = 1 - p = 1 - 0.22 = 0.78

n = 120

Using binomial distribution,

= n * p = 120 * 0.22 = 26.4

= n * p * q = 120 * 0.22 * 0.78 = 4.53784

Using continuity correction ,

P(31.5 < x < 32.5) = P((31.5 - 26.4)/ 4.53784) < (x - ) / < (32.5 - 26.4) / 4.53784) )

= P(1.1239 < z < 1.3443)

= P(z < 1.3443) - P(z < 1.1239)

= 0.9106 - 0.8695

= 0.0411

Probability = 0.0411.

The probability that exactly 32 of 120 eligible voters voted is 0.0411