Question

A survey showed that 34 ​% of human resource professionals are at companies that rejected job candidates because of information found on their social media. If 27 human resource professionals are randomly​ selected, would 16 be a significantly high number to be at companies that rejected job candidates because of information found on their social​ media? Why or why​ not?

Answer 1

Using the binomial distribution, it is found that since 16 is more than 2.5 standard deviations above the mean, it is a unusually high number.

What is the binomial probability distribution?

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

A measure is considered to be unusually high if it is more than 2.5 standard deviations above the mean.

In this problem, we hav ehtat:

• 34% of companies reject candidates because of information found on their social media, hence p = 0.34.

• 27 human resource professionals are randomly​ selected, hence n = 27.

Then, we find the threshold for unusually high values as follows:

E(X) = np = 27 x 0.34 = 9.18

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{27(0.34)(0.66)} = 2.46$

T = 9.18 + 2 x 2.46 = 14.1.

Since 16 is more than 2.5 standard deviations above the mean, it is a unusually high number.

More can be learned about the binomial distribution at brainly.com/question/24863377

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