Question

1. The mean triglyceride level for U.S. adults (ages 20 and older) is 97 milligrams per deciliter. Assume the triglyceride levels of U.S. adults who are at least 20 years old are normally distributed, with a standard deviation of 25 milligrams per deciliter. You randomly select a U.S. adult who is at least 20 years old. What is the probability that the person triglyceride level is less than 100? (Levels under 150 milligrams per deciliter are considered normal).

2. In a randomly selected sample of women ages 20-34 the mean total cholesterol level is 179 milligrams per deciliter with a standard deviation of 38.9 milligrams per deciliter. Assume the total cholesterol levels are normally distributed. Find the highest total cholesterol level a woman in this 20-34 age group can have and still be in (the bottom 1%).

Answer 1

1) P(X < 100)

= P((X - )/ < (100 - )/)

= P(Z < (100 - 97)/25)

= P(Z < 0.12)

= 0.5478

2) P(X < x) = 0.01

Or, P((X - )/ < (x - )/) = 0.01

Or, P(Z < (x - 179)/38.9) = 0.01

Or, (x - 179)/38.9 = -2.33

Or, x = -2.33 * 38.9 + 179

Or, x = 88.363