Part A. Make sure you answer all parts of this question and show your reasoning for each part.
Calculate, report and draw conclusions:
In a recent election, 45% of the voters were Republican, and the rest were not. Of the Republicans, 70% voted for Candidate Smith, and of the non-Republicans, 10% voted for Candidate Smith.
a. Suppose we select a random voter on her way out of the voting booth. Write the values for these probabilities:
i. P(voter is Republican)
ii. P(voter is not Republican)
iii. P(voted for Smith|voter is Republican)
iv. P(voted for Smith|voter is not Republican)
b. Find P(Republican and voted for Smith) and write a complete sentence about what that probability means.
c. Find P(not Republican and voted for Smith) and write a complete sentence about what that probability means.
d. Find P(voted for Smith). (Hint: (b) and (c) cover all of the possibilities for how voting for Smith can happen.)
Part B. Blood pressure is usually measured as two numbers. The higher number is called the systolic blood pressure, and reflects the pressure of the blood on the walls of the arteries when the heart contracts (at the moment of the heartbeat). Blood pressure is measured in units of millimeters of Mercury (abbreviated mmHg).
In a particular population of adult men, systolic blood pressure is normally distributed with a mean of 112 mmHg and a standard deviation of 8 mmHg.
Blood pressure is typically assessed using the values in following table:
| Systolic blood pressure |
Diagnosis |
| Less than 90 |
Low |
| 90-120 |
Normal |
| 120-140 |
Borderline high |
| 140 and above |
High |
A man is chosen at random from the population.
a. What is the probability that his blood pressure is either borderline high or high:
i. Follow the steps for part a, but be sure to pull down the dropdown menu on the Probability line to change <= (less than or equal) to >= (greater than or equal). To find this probability, what value does the blood pressure need to be greater than or equal to?
Calculate, report and draw conclusions:
c. What is the probability that his blood pressure is either below 90 or above 120?
d. What is the probability that his blood pressure is normal (between 90 and 120)?
i. Hint 1: This is the complement of his blood pressure being not normal, so you can use the results of part c.