Consider the population that consists of all soft contact lenses made by a particular manufacturer, and define the variable x 5 thickness (in millimeters). Suppose that a reasonable model for the population distribution is the one shown in the following figure:

Density 0 0.20 Thickness 5

0.40

a. Verify that the total area under the density curve is equal to 1. [Hint: The area of a triangle is equal to 0.5(base)(height).]

b. What is the probability that x is less than .20? less than .10? more than .30?

c. What is the probability that x is between .10 and

.20? (Hint: First find the probability that x is not between .10 and .20.)

d. Because the density curve is symmetric, the mean of the distribution is .20. What is the probability that thickness is within 0.05 of the mean thickness?