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Sagot :
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:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
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
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{27(0.34)(0.66)} = 2.46[/tex]
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 https://brainly.com/question/24863377
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