Answer :
Using the binomial distribution, the mean and the standard deviation of the amounts are given as follows:
- Mean: 1.37.
- Standard deviation: 1.16.
What are the mean and the standard deviation of the binomial distribution?
The binomial distribution gives the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The mean is given by the following rule:
E(x) = np.
The standard deviation is given by the following rule:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In the context of this problem, the parameters are found as follows:
- p = 0.01, as about 1% of the population has a particular genetic mutation.
- n = 137, as 137 people are randomly selected.
Hence the mean and the standard deviation are, respectively, given by:
- E(x) = np = 137 x 0.01 = 1.37.
- [tex]\sqrt{V(X)} = \sqrt{137(0.01)(0.99)} = 1.16[/tex]
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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