Question

Use a normal approximation to find the probability of the indicated number of voters. In this​ case, assume that 129 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 31 voted.

The probability that fewer than 31 of 129 eligible voters voted is?

Answer 1

Solution:

Given that,

P = 0.22

1 - P = 0.78

n = 129

Here, BIN ( n , P ) that is , BIN (129 , 0.22)

then,

n*p = 129 * 0.22 = 28.38

n(1- P) = 129 * 0.78 = 100.62

According to normal approximation binomial,

X Normal

Mean = = n*P = 28.38

Standard deviation = =n*p*(1-p) = 22.1364

We using continuity correction factor

P(X < a ) = P(X < a - 0.5)

P(x < 30.5) = P((x - ) / < (30.5 - 28.38) / 22.1364 )

= P(z < 0.45)

Probability = 0.6736