Question

Use a normal approximation to find the probability of the indicated number of voters. In this​ case, assume that 170 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 43 voted.

The probability that fewer than 43 of 170 eligible voters voted is

Answer 1

Solution:

Given that,

P = 0.22

1 - P = 0.78

n = 170

Here, BIN ( n , P ) that is , BIN (170 , 0.22)

then,

n*p = 170*0.22 = 37.4 > 5

n(1- P) = 170*0.78 = 132.6 >5

According to normal approximation binomial,

X Normal

Mean = = n*P = 37.4

Standard deviation = =n*p*(1-p) = 170*0.22*0.78 = 28.172

We using countinuity correction factor

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

P(x < 42.5) = P((x - ) / < (42.5 - 37.4) / 28.172)

= P(z < 0.961)

= 0.8317

The probability that fewer than 43 of 170 eligible voters voted is 0.8317