Question

Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 182 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 182 eligible voters voted is _______ 

Answer 1

Given that,

p = 0.22

q = 1 - p =1 - 0.22=0.78

n = 182

Using binomial distribution,

$\mu$ = n * p = 182*0.22=40.04

$\sigma$ = $\sqrt$ n * p * q = $\sqrt$ 182*0.22*0.78=5.5885

Using continuity correction ,

P(42.5< x <43.5 )= P[(42.5 - 40.04)/ 5.5885) < (x - $\mu$ ) / $\sigma$ < (43.5 - 40.04) / 5.5885]

= P(0.44 < z < 0.59)

= P(z <0.59 ) - P(z < 0.44)

=0.7224 -0.6700

=0.0524