Question

It is generally believed that nearsightedness affects about 1212​% of children in a certain region. A school district tests the vision of 160160 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

Explanation:

Total number of kindergarten children in that region that were tested is 160

It is generally believed that nearsightedness affects about 12% of children in a certain region. Therefore,

The expected number of kindergarten children expected to be​ nearsighted is

12/100 × 160 = 19

Probability of success, p = 0.12

Probability of failure, q = 1 - p = 1 - 0.12 = 0.88

Standard deviation = √npq = √(160 × 0.12 × 0.88) = 4.11