Question

The probability that an individual has​ 20-20 vision is 0.160.16. in a class of 4040 ​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

The mean is 6.4 and the standard deviation is 2.319.

The mean of a binomial distribution is given by

μ = np = 40(0.16) = 6.4

The standard deviation is given by
σ = √(n)(p)(1-p) = √40(0.16)(0.84) = √5.376 = 2.319