Question

A transit authority offers discount rates to companies that have at least 30 employees who use public transportation to get to work. There are 542 employees in a company. What is the probability that the company will not get the discount?

Can the normal distribution be used to approximate the binomial distribution?

What is the probability that the company will not get the discount? (Round to four decimal places)

Answer 1

This is a binomial distribution question with

n = 542

p = 0.05

q = 1 - p = 0.95

This binomial distribution can be approximated as Normal distribution since

np > 5 and nq > 5

Since we know that

Both are more than 5 so we can use the approximation

x = 29.5

from continuity correction

P(x < 29.5)=?

The z-score at x = 29.5 is,

z = 0.473

This implies that

P(x < 29.5) = P(z < 0.473) = {0.6819}

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