Question

It is generally believed that nearsightedness affects about 13​% of children in a certain region. A school district tests the vision of

178 incoming kindergarten children. How many would be expected to be​ nearsighted? What is the standard deviation for the number of nearsighted children in this​ group?

Answer 1

Let X denote the number of nearsighted children in the sample.

Then $X\sim Bin(n=178,p=0.13)$

Expected value = $E(X)=np=(178)(0.13)=23.14\approx 23$

Standard deviation = $\sqrt{V(X)}=\sqrt{np(1-p)}=\sqrt{178(0.13)(1-0.13)}=4.4868\approx 5$