There are two types of cholesterol: low-density lipoprotein cholesterol (LDL, al
ID: 3129875 • Letter: T
Question
There are two types of cholesterol: low-density lipoprotein cholesterol (LDL, also called “bad” cholesterol) and high-density lipoprotein cholesterol (HDL, also called “good” cholesterol). The lower the LDL cholesterol level, the healthier the person is. Suppose the LDL cholesterol level in the general population is normally distributed with a mean of 140 and a standard deviation of 32.
a) If an LDL level below 160 is considered as acceptable, what percentage of people have an acceptable LDL level?
b) If an LDL level above 190 is considered as dangerous, what percentage of people have a dangerous LDL level?
c) If an LDL level between 160 and 190 means the person should start taking preventive actions, what percentage of people need preventive actions?
d) If an LDL level below 100 is considered as optimal, what percentage of people have an optimal LDL level?
e) If an LDL level below 115 is considered as healthy, what percentage of people have a healthy but NOT optimal LDL level?
f) Tom’s LDL level is higher than 65% of people in the population. What is Tom’s LDL level?
g) Jerry’s LDL level is on the 80th percentile. What is Jerry’s LDL level?
h) Eric’s LDL level is on the 40th percentile, what is Eric’s LDL level?
i) If we randomly select a person from the population, what is the probability of this person’s LDL level being exactly equal to 195?
j) If we convert people’s LDL levels into Z scores, what is the mean of those Z scores?
k) If we convert people’s LDL levels into Z scores, what is the variance of those Z scores?
l) What is the median LDL level in the general population?
(Questions e-l only)
Explanation / Answer
a)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 160
u = mean = 140
s = standard deviation = 32
Thus,
z = (x - u) / s = 0.625
Thus, using a table/technology, the left tailed area of this is
P(z < 0.625 ) = 0.734014471 = 73.40% [ANSWER]
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b)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 190
u = mean = 140
s = standard deviation = 32
Thus,
z = (x - u) / s = 1.5625
Thus, using a table/technology, the right tailed area of this is
P(z > 1.5625 ) = 0.059085123 = 5.91% [ANSWER]
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C)
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 160
x2 = upper bound = 190
u = mean = 140
s = standard deviation = 32
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = 0.625
z2 = upper z score = (x2 - u) / s = 1.5625
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.734014471
P(z < z2) = 0.940914877
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.206900406 = 20.69% [ANSWER]
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d)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 100
u = mean = 140
s = standard deviation = 32
Thus,
z = (x - u) / s = -1.25
Thus, using a table/technology, the left tailed area of this is
P(z < -1.25 ) = 0.105649774 = 10.56% [ANSWER]
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