Question

Thirty-two percent of workers in Troberca City are college graduates. You randomly select 50 workers and ask them is he or she is a
college graduate. Find the probability that less than 18 workers are college graduate. (Approximating a Binomial Distribution)
(A) 32.6%
B 67.4%
64.0%
36.0%

Answer 1

B around 68% would be college graduates

Answer 2

The correct option is B) 67.4%

What is the z- score table?

A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution. Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean.

Given here, P(probability that a worker is a college graduate) = 32%

                                                                                                      = 0.32

q (probability that a worker is not a college graduate) is 1-0.32 = 0.68  

now μ(mean) = n×p

                      = 50×0.32

                      = 16

Again standard deviation σ = $\sqrt{npq\\}$

                                           σ = $\sqrt{50\cdot 0.32\cdot 0.68}$

                                           σ = 3.2985

now P(x<17.5) = P((x-μ)/σ <(17.5-16)/3.2985)

                      = P(z<0.45)  

                      = 0.674 [using z table]

                      = 67.4%

Hence option 2 is the correct answer

Learn more about z-table here:

brainly.com/question/29283457

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