Degrees: Physiotheraphy
Date: May 19, 2017

# Probability and random variables

## Question 1

The prevalence of sciatica in a population is 3%. The Lasegue’s test is a neurotension test that is used to diagnose the sciatica with a sensitivity of 91% and a specificity of 26%. On the other hand, there is an alternative test with a sensitivity of 80% and a specificity of 90%.

1. Compute the positive predictive value for the Lasegue’s test.
2. Assuming that the tests are independent, compute the probability of having a positive outcome in both tests.
3. Compute the probability of getting a wrong diagnose in the Lesegue’s test or in the alternative test.
4. Which test is better as a screening test (to rule out the sciatica)?

## Question 2

A physiotherapist opens a clinic and use the social networks to advertise it. In particular he send a friend request to 20 contacts on Facebook. If the probability that a Facebook user accept the friend request is 80%, what is the probability that more than 18 accept the friend request? What is the expected number of friend requests accepted?

## Question 3

According to a study of the Information Society of Spain in 2013, the spanish checks the mobile phone 150 times a day in average. What is the probability that a spanish person checks the mobile phone more than 2 times an hour?

## Question 4

The the cervical rotation in a population follows a normal probability distribution model with mean 58º and standard deviation 6º.

1. Between what values are the cervical rotation of the central 50\% of the population?
2. Taking into account the precision of the measurement instrument, a goniometer, a rotation less than 53º is considered a mobility limitation. If we take a random sample of 100 persons from this population, what is the expected number of persons with mobility limitation in the sample?