Question

Use a normal approximation to find the probability of the indicated number of voters. In this​ case, assume that 119 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

Answer 1

Solution :

Given that,

p = 0.22

q = 1 - p =1 - 0.22=0.78

n = 119

Using binomial distribution,

Mean = = n * p = 119 * 0.22=26.18

Standard deviation = = n * p * q =  119 *0.22 * 0.78=4.5189

Using continuity correction ,

P( X <29.5) = P(x - ) / < (29.5 - 26.18) / 4.5189)

= P(z < 0.73)

Probability = 0.7673