Question

The probability that an individual has​ 20-20 vision is 0.19. In a class of 40 ​students, what is the mean and standard deviation of the number with​ 20-20 vision in the​ class? Round to the nearest thousandth.

Answer 1

7.6, 2.4211

Explanation:

Given that the probability that an individual has​ 20-20 vision is 0.19.

No of class students =n=40

p = 0.19 and q = 1-0.19 = 0.81

Since each student is independent of the other and there are two outcomes either 20-20 vision or no, we find that X the no of students having 20-20 vision is binomial with n =40 and p = 0.19

Mean
`= E(X) = np =\\40(0.19)\\=7.6`

Variance of X = npq =
`40(0.19)(0.81) = 6.156\\`

Std deviation = square root of variance =2.4811