Question

In a certain city it is known that 20% of the residents have a vehicle and the rest do not. If we take a sample of 256 people. What is the probability that the percentage of people who have vehicles is greater than 25%? What is the probability that the percentage of people who have vehicles is between 15% and 25%?

Answer 1

This is a binomial distribution question with
n = 256
p = 0.20
q = 1 - p = 0.8
This binomial distribution can be approximated as Normal distribution since
np > 5 and nq > 5

Since we know that


a) 25% of 256 = 0.25*256 = 64
P(x > 64.0)=?
The z-score at x = 64.0 is,

This implies that


b)
x1 = 15% of 256 = 0.15*256 = 38.4
x2 = 25% of 256 = 0.25*256 = 64

P(38.4 < x < 64.0)=?

This implies that


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