Question

In the past presidential election, the actual voter turnout was 70%. In a survey, 435 students were asked if they voted in the election. (a) Find the mean and standard deviation for the number of actual voters in the group of 435 students (b) In the survey of 435 students, 280 said that they voted. Is this result consistent with actual voter turnout?Why or why not?

Answer 1

This is a binomial distribution question with

n = 435

p = 0.70

q = 1 - p = 0.300

This binomial distribution can be approximated as Normal distribution since

np > 5 and nq > 5

a)

Since we know that

Type of this part: 1

b) x = 280

P(x < 280.0)=?

The z-score at x = 280.0 is,

z = -2.5634

This implies that

P(x < 280.0) = P(z < -2.5634) = {0.0052}

No, as it has very less probability that only 280 voted