Question

Suppose that 80% of all registered California voters favor banning the release of information from exit polls in presidential elections until after the polls in California close. A random sample of 25 registered California voters is selected.

Required:
a. Calculate the mean and standard deviation of the number of voters who favor the ban.
b. What is the probability that exactly 20 voters favor the ban?

Answer 1

a. Mean = 20

Sd = 4

b. Probability of X = 20 = 0.1960

Explanation:

we have

n = 25

p = 80% = 0.8

mean = np

= 0.8 * 25

= 20

standard deviation = √np(1-p)

= √25*0.8(1-0.8)

=√4

= 2

probability that exactly 20 favours ban

it follows a binomial distribution

= 25C20 × 0.8²⁰ × 0.2⁵

= 53130 × 0.01153 × 0.00032

= 0.1960

Probability of X = 20 = 0.1960