20 BME 3060: INTRODUCTION TO BIOSTATISTICS
H/W #7
ON NORMAL DISTRIBUTION
Theme: How to do calculations with normal distribution? It may be helpful to draw
an appropriate diagram to have a handle on the problem.
Blood Pressure Model
According to the National Health Survey, systolic blood pressures of 18- to 74-
year-old males in the United States are normally distributed with mean 129
millimeters of mercury (mm Hg) and standard deviation 19.8 mm Hg.
1. Determine the quantile q of the distribution of the systolic blood pressures
such that 95% of the population has systolic blood pressure ≤ q.
2 points
Code: qnorm(.95, 129, 19.8, lower.tail = T)
Answer: [1] 161.5681
2. What percentage of the population has systolic blood pressure ≤ 90 mm Hg?
2 points
Code: pnorm(90, 129, 19.8, lower.tail = T)
Answer: [1] 0.02443656
3. What percentage of the population has systolic blood pressure between 110
and 150 mmHg? 2 points
Code: x= pnorm(150, 129, 19.8)-pnorm(110, 129, 19.8)
x= [1] 0.6869362
Framingham study and Cholesterol Models
In the Framingham Study, serum cholesterol levels were measured for a large
number of healthy males. The population was then followed for 16 years. At the
end of this time, the men were divided into two groups: those who developed
coronary heart disease and those who had not. Among those who developed heart
disease, the initial cholesterol levels were normally distributed with mean μ =
244 mg/100 ml and standard deviation σ = 51 mg/100 ml. Among those who did
not develop the disease, the initial chol