Question

Q1-Q7. One type of cholesterol is called low-density lipoprotein cholesterol (LDL, also called the “bad” cholesterol). Adults should check their cholesterol levels at least every 5 years. The lower the LDL cholesterol is, the healthier the person is. Suppose the LDL cholesterol scores in men follow a normal distribution N(µ = 140, σ = 32).

1. If an LDL level below 160 is considered as acceptable, what percent of men have an acceptable cholesterol level?

Note the answer field below does not accept the percentage symbol "%", so fill in your answer with number only and without the "%" mark. For example, if your answer is "12.3456%" then put "12.3456" in the field below. Use the same format for all the questions in this HW.

2. If an LDL level above 190 is considered as dangerous, what percent of men have a dangerous cholesterol level?

3. If an LDL level between 160 and 190 means the man should start taking preventive actions, what percent of men need preventive actions?

Answer 1

Let X :-   Cholesterol levels

Part 1.

If an LDL level below 160 is considered as acceptable, what percent of men have an acceptable cholesterol level?

P ( X < 160 )

Standardizing the value

P ( X < 160 ) = P ( Z < 0.63 )

P ( X < 160 ) = 0.7340

To find the percentage 0.7340 * 100 = 73..40%

Part 2. If an LDL level above 190 is considered as dangerous, what percent of men have a dangerous cholesterol level?

P ( X > 190 ) = 1 - P ( X < 190 )

Standardizing the value

P ( X > 190 ) = 1 - P ( X < 190 )

P ( X > 190 ) = 1 - P ( Z < 1.56 )

P ( X > 190 ) = 1 - 0.9409

P ( X > 190 ) = 0.0591

To find the precentage 0.0591 * 10 = 5.91%

Part 3. If an LDL level between 160 and 190 means the man should start taking preventive actions, what percent of men need preventive actions?

P ( 160 < X < 190 )

P ( 0.63 < Z < 1.56 )

P ( Z < 1.56 ) - P ( Z < 0.63 )

P ( 160 < X < 190 ) = P ( Z < 1.56 ) - P ( Z < 0.63 )

P ( 160 < X < 190 ) = 0.9409 - 0.7340

P ( 160 < X < 190 ) = 0.2069

To find the precentage 0.2069 * 100 = 20.69%