Degrees: Pharmacy, Biotechnology

Date: November 19, 2018

## Question 1

In a population that is exposed to two viruses strains $A$ and $B$ it is known that 2% of persons are immune only to virus $A$ and 4% are immune only to virus $B$. On the other hand it is known tha 91% of the population would be infected by some of the two viruses.

- What is the probability that a person is immune to the two viruses?
- What is the probability that a person immune to virus $A$ is infected by virus $B$?
- Are dependent the events of being immune to the two viruses?

## Question 2

In a study about the blood pressure the systolic pressure of 2400 males older than 18 was measured. It was observed that 640 had a pressure greater than 14 mmHg and 1450 had between 10 and 14 mmHg. Assuming that the systolic pressure in males older than 18 is normally distributed,

- Compute the mean and the standard deviation.
- Compute how many males had a systolic pressure between 11 and 13 mmHg.
- Compute the value of the systolic pressure such that there was 300 males with a systolic pressure above it.

## Question 3

The average number of people that enters the intensive care unit of a hospital in an 8-hours shift is $1.4$.

- Compute the probability that a day enter more than 3 persons in the ICU.
- Compute the probability that in a week there are more than one day with less than 3 persons entering the ICU.

## Question 4

Two hospitals use different tests $A$ and $B$ to detect a streptococcal infection. The tables below show the results of applying these tests in each hospital during the last year.

- Compute the probability of a correct diagnostic with test $A$.
- Compute the positive predicted value of test $A$.
- Compute the negative predicted value of test $B$.
- How can these tests be combined to reduce the risk of wrong diagnosis?