Pharmacy exam 2022-01-17

Degrees: Pharmacy, Biotechnology
Date: January 17, 2022

Question 1

A diagnostic test for a disease with a prevalence of 10% has a positive predictive value of 40% and negative predictive value of 95%.

1. Compute the sensitivity and the specificity of the test.

2. Compute the probability of a right diagnose.

3. What must be the minimum sensitivity of the test to be able to diagnose the disease?

Question 2

To study the effectiveness of two antigen tests for the COVID both tests have been applied to a sample of 100 persons. The table below shows the results:

$$\overline{)\begin{array}{ccr}\text{Test }A& \text{Test }B& \text{Num persons}\\ \text{+}& \text{+}& 8\\ \text{+}& \text{-}& 2\\ \text{-}& \text{+}& 3\\ \text{-}& \text{-}& 87\end{array}}$$

Define the following events and compute its probabilities:

1. Get a $+$ in the test $A$.

2. Get a $+$ in the test $A$ and a $-$ in the test $B$.

3. Get a $+$ in some of the two tests.

4. Get different results in the two tests.

5. Get the same result in the two tests.

6. Get a $+$ in the test $B$ if we got a $+$ in the test $A$.

Are the outcomes of the two tests independent?

Question 3

It is known that the life of a battery for a peacemaker follows a normal distribution. It has been observed that 20% of the batteries last more than 15 years, while 10% last less than 12 years.

1. Compute the mean and the standard deviation of the battery life.

2. Compute the fourth decile of the battery life.

3. If we take a sample of 5 batteries, what is the probability that more than half of them last between 13 and 14 years?

4. If we take a sample of 100 batteries, what is the probability that some of them last less than 11 years?