Assignment 2 (Probability)


Spring 2021

Due Monday May 24th, 2021


1. The following table displays blood pressure status by sex.

Optimal Normal Hypertension Total

Male 22 73 55 150

Female 43 132 65 240

Total 65 205 120 390

a. What proportion of the participants has optimal blood pressure?

b. What proportion of men has optimal blood pressure?

c. What proportion of participants with hypertension is male?

d. Are hypertensive status and male gender independent?


2. Diastolic blood pressures are assumed to follow a normal distribution with a mean of 85 and

a standard deviation of 12.

a. What proportion of people has diastolic blood pressures less than 90?

b. What proportion has diastolic blood pressures between 80 and 90?

c. If someone has a diastolic blood pressure of 100, what percentile does this represent?

3. Consider the data described in Problem 2. If a sample of 15 participants are sampled, what is

the probability that their mean diastolic blood pressure exceeds 90?


4. A large national study finds that 10% of pregnant women deliver prematurely. A local

obstetrician is seeing 16 pregnant women in his next clinic session.

a. What is the probability that none will deliver prematurely?

b. What is the probability that fewer than 3 will deliver prematurely?

c. What is the probability that none will deliver prematurely if, in fact, the true percentage

who deliver prematurely is 5.5%?

d. If the true percentage is 10% and this obstetrician has 146 pregnant women under his

care, how many would be expected to deliver prematurely?

5. Diastolic blood pressures are approximately normally distributed with a mean of 75 and a

standard deviation of 10.

a. What is the 90th percentile of diastolic blood pressure?

b. If we consider samples of 20 patients, what is the 90th percentile of the mean diastolic

blood pressure?

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