Respuesta :
By using Binomial Distribution the probability that exactly 6 workers take the bus to work is 0.001.
What is Binomial Distribution?
When every experiment shares the probability of achieving a given value, the number of trials or observations is summarised using the binomial distribution.
The likelihood of observing a specific percentage of successful occurrences in a specific number of trials is determined by the binomial distribution.
The formula for binomial distribution is-
[tex]P(X=x)={ }^{n} C_{k} p^{k}(1-p)^{n-k}[/tex]
'p' is the probability of success,
(1-p) is probability of failure,
'n' is the number of workers,
'k' is number of given workers.
According to the question,
Calculate the probability of success as;
[tex]p=\frac{15}{100}=0.15[/tex]
The, the probability of the failure becomes;
[tex](1-p)=1-0.15=0.85[/tex]
Put above two value in formula of binomial theorem to get the value.
[tex]{ }^{10} C_{6}(0.15)^{6}(0.85)^{4}=0.001[/tex]
Therefore, the probability that exactly 6 workers take the bus to work is 0.001.
To know more about the binomial probability, here
https://brainly.com/question/9325204
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