Question

The probability that an individual has​ 20-20 vision is 0.19 0.19. in a class of 70 70 ​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

Formula to find mean and standard deviation is,

Means = np and standard deviation =$\sqrt{n p (1-p)}$.

Where n= sample size, p = probability.

According to the given problem, the probability that an individual has​ 20 vision is 0.19 in a class of 70 ​students. So,

p = 0.19 and n = 70.

Hence, the first step is to plug in these values in the above formula to get mean and standard deviation. Therefore,

Mean = np

= 70* 0.19

= 13.3

= 13.300 (Rounded to nearest thousandth.

Standard deviation = $\sqrt{np(1-p)}$

=$\sqrt{70*0.19*(1-0.19)}$

=$\sqrt{13.3*0.81}$

=√10.773

=3.282224855

= 3.282 (Rounded to nearest thousandth).