Question

6.6.11

Use a normal approximation to find the probability of the indicated number of voters. In this​ case, assume that 187 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 43 voted The probability that exactly 43 of 187 eligible voters voted is

Answer 1

Solution :

Using binomial distribution,

= n * p = 187 * 0.22 = 41.14

= n * p * q = 187 * 0.22 * 0.78 = 5.6647

Using continuity correction ,

= P[(42.5 - 41.14)/ 5.6647) < (x - ) / < (43.5 - 41.14) / 5.6647]

= P(-0.24 < z < 0.24)

= P(z < 0.24) - P(z < -0.24)

= 0.1897