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Probability: Cholesterol, Smoking and Hyperlipidemia

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1. The following box-whisker plot shows the distributions of total cholesterol levels in boys and girls 10-15 years of age.
(see the attachment for the box-whisker plot)

A. What is the median total cholesterol level in boys? ________
B. What is Q1 for boys? ________
C. What is Q3 for boys? ________
D. Lower Limit for Outliers for boys: ________
E. Upper Limit for Outliers boys: ________
F. Are there any outliers in total cholesterol in boys? ________
G. What proportions of the boys have total cholesterol less than 205? _______ %
H. What proportions of the girls have total cholesterol less than 205? _______ %

2. As part of a study, investigators wanted to assess the accuracy of self-reported smoking status. Participants are asked whether they currently smoke or not. In addition, laboratory tests are performed on hair samples to determine presence or absence of nicotine. The laboratory assessment is considered the gold standard, or truth about nicotine. The data are as follows:

Nicotine Absent Nicotine Present
Self-Reported Non-Smoker 82 14
Self-Reported Smoker 12 52

A. What is the sensitivity of self-reported smoking status?

B. What is the specificity of self-reported smoking status?

3. A recent study reported that the prevalence of hyperlipidemia (defined as total cholesterol over 200) is 30% in children 2-6 years of age. If 12 children are analyzed,

A. What is the probability that at least 3 are hyperlipidemic?

B. What is the probability that 3 are hyperlipidemic?

C. How many would be expected to meet the criteria for hyperlipidemia?

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Solution Summary

Step-by-step solutions are provided for each question, finding medians, upper and lower limits for outliers, and sensitivity, and probability for the variety of questions.

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1. The following box-whisker plot shows the distributions of total cholesterol levels in boys and girls 10-15 years of age.

A. What is the median total cholesterol level in boys? ___205_____
In the box-whisker plot for Boys, locate the position of the vertical line in the middle of the rectangle.

B. What is Q1 for boys? ___175_____
In the box-whisker plot for Boys, locate the position of the vertical line on the left side of the rectangle.

C. What is Q3 for boys? ___245_____
In the box-whisker plot for Boys, locate the position of the vertical line on the right side of the rectangle.

D. Lower Limit for Outliers for boys: ___70_____
IQR = Q3 - Q1 = 245 - 175 = 70
Lower Limit for Outliers = Q1 - 1.5*IQR = 175 - 1.5*70 = 70

E. Upper Limit for Outliers boys: ___350_____
IQR = Q3 - Q1 = 245 - 175 = 70
Upper ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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  • "Hello, thank you for your answer for my probability question. However, I think you interpreted the second and third question differently than was meant, as the assumption still stands that a person still independently ranks the n options first. The probability I am after is the probability that this independently determined ranking then is equal to one of the p fixed rankings. Similarly for the third question, where the x people choose their ranking independently, and then I want the probability that for x people this is equal to one particular ranking. I was wondering if you could help me with this. "
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