Suppose that p(x) is the density function for heights of american men, in inches, and suppose that p(69)=0.19. think carefully about what the meaning of this mathematical statement is. (a) approximately what percent of american men are between 68.6 and 69.4 inches tall?

Using continuity correction, it is found that 19% of American men are between 68.6 and 69.4 inches tall.

A density function traditionally represents a discrete probability distribution.

If we want a continuous distribution to be represented, continuity correction is used, which means that the following equality holds:

In this problem, we are given:

Applying continuity correction:

Thus, 19% of American men are between 68.6 and 69.4 inches tall.

A similar problem, in which continuity correction is used, is given at link

15,2% of American men are between 68.6 and 69.4 inches tall.

Step-by-step explanation:

p(69)=0.19 tells you that 19% of all American men are 69in tall. Now, we want to know what percentage of those men are exactly between 68.6 and 69.4 inches tall. We only need to multiply the given density function by the gap between the two heights we are looking for, so:

0.19 * (69.4-68.6) = 0.19*0.8 = 0.152*100 = 15,2%