Physiotherapy exam 2016-05-13
Grade: Physiotherapy
Date: May 13, 2016
Question 1
Of all the anterior cruciate ligament of the knee injuries, the rupture occurs in 20% of cases, and to detect it there are three different tests:
- The drawer test that analyzes the stability of the tibia. It has a sensitivity of 80% and a specificity of 0.99%.
- A radiologic study in 2 planes, that allows rule out bone avulsion. It has a sensitivity of 0.85% and a specificity of 0.9%.
- A magnetic resonance, that it is the most appropriate when there is hematoma. It has a sensitivity and a specificity of 0.98%.
Assuming that the tests are independent,
- Compute the predictive values of the drawer test.
- If an individual has an anterior cruciate ligament injury, what is the probability that the radiologic study and the magnetic resonance return a positive outcome?
- If an individual has an anterior cruciate ligament injury, what is the probability that the radiologic study or the magnetic resonance give a wrong diagnosis?
- $PPV_1 = P(D\vert +_1) = 0.9524$ and $NPV_1=P(\bar D\vert -_1)=0.9519$.
- $P(+_2)=0.25$, $P(+_3)=0.212$ and $P(+_2\cap +_3)=0.053$.
- $P(\mbox{Error}_2)=0.11$, $P(\mbox{Error}_3)=0.02$ and $P(\mbox{Error}_2\cup \mbox{Error}_3)=0.1278$.
Question 2
It is known that 10% of professional soccer players have a cruciate ligament injury during the league. It is also known that the ligament rupture occurs in 20% of cruciate ligament injuries.
- Calculate the probability that in a team with 20 players more than 3 have a cruciate ligament injury during the league.
- Calculate the probability that in a league with 200 players more than 3 have a ligament rupture.
- Naming $X$ to the number of players in a team with a cruciate ligament injury, $P(X>3)=0.133$.
- Naming $Y$ to the number of players in a league with a ligament rupture, $P(Y>3)= 0.5665$.
Question 3
In a blood analysis the LDL cholesterol level reference interval for a particular population is $(42,155)$ mg/dl. (The reference interval contains the 95% of the population and is centered in the mean).
Assuming that the LDL cholesterol level follows a normal distribution,
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Calculate the mean and the standard deviation of the LDL cholesterol level.
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According to the LDL cholesterol level, patients are classified into three categories of infarct risk:
LDL cholesterol level Infarct risk Less than 100 mg/dl Low Between 100 and 160 mg/dl Medium Greater than 160 mg/dl High Calculate the percentage of people in the population that falls into every category of infarct risk.
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The probability of having an infarct with a high risk is twice the probability of having infarct with a medium risk, and this is twice the probability of having infarct with a low risk. What is the probability of having infart in the whole population if the probability of having infarct with a low risk is 0.01?
Naming $C$ to the LDL cholesterol level,
- $\mu=98.5$ mg/dl and $\sigma=28.25$ mg/dl.
- $P(\mbox{Low})=P(C<100)=0.5199$, $P(\mbox{Medium})=P(100\leq C\leq 160)=0.4654$ and $P(\mbox{Low})=P(C>160)=0.0146$. Thus, there are 51.99% of persons with low risk, 46.54% of persons with medium risk and 1.46% of persons with high risk.
- Naming $I$ to the event of havig an infarct, $P(I)=0.0151$.