Question

Suppose that p(x) is the density function for heights of American men, in inches, and suppose that p(69)=0.2. Think carefully about what the meaning of this mathematical statement is. (a) Approximately what percent of American men are between 68.8 and 69.2 inches tall? Approximately .2 percent. (b) Suppose that the average height of American men is 69 inches. Would you expect p(78)>p(69) or p(78)

p(69) B. p(78)

Answer 1

(a) p(68.8 to 69.2) = 8%

(b) p(78) < p(69)

Explanation:

p(x) is the density function for heights of American men.

Suppose that p(69)=0.2

Think carefully about what the meaning of this mathematical statement is!

The meaning of this mathematical statement is that 20% of American men are 69 inches tall or shorter than that.

(a) Approximately what percent of American men are between 68.8 and 69.2 inches tall?

p(68.8 to 69.2) = p(69)*(69.2 - 68.8)

p(68.8 to 69.2) = 0.2*(0.4)

p(68.8 to 69.2) = 0.08 = 8%

Therefore, 8% of American men are between 68.8 and 69.2 inches tall.

(b) Suppose that the average height of American men is 69 inches.

Would you expect p(78) > p(69) or p(78) < p(69) ?

The probability of American men having a height of 69 inches will be greater than American men having a height of 78 inches.

p(78) < p(69)