Respuesta :
Using the binomial distribution, it is found that:
- The mean of the number of left-handers in the class is of 1.6.
- The standard deviation of the number of left-handers in the class is 1.16.
For each student, there are only two possible outcomes, either they are left-handers, or they are not. The probability of a student being a left-hander is independent of any other student, hence the binomial distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value is:
[tex]E(X) = np[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In this problem:
- The probability that an individual is left-handed is 0.16, hence [tex]p = 0.16[/tex].
- The class has 10 students, hence [tex]n = 10[/tex]
Then:
[tex]E(X) = np = 10(0.16) = 1.6[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10(0.16)(0.84)} = 1.16[/tex]
You can learn more about the binomial distribution at https://brainly.com/question/24863377
