It is estimated that 80% of people in Cyprus take paracetamol for headache treatment. Out of 5 having headache, find the probability that exactly 2 will take paracetamol.

Question

It is estimated that 80% of people in Cyprus take paracetamol for headache treatment. Out of 5 having headache, find the probability that exactly 2 will take paracetamol.

Answer 1

Hi, thanks for posting your question. Based on this question, I'd solve it as follows:

1. Identify if this is a discrete or continuous random variable - this is a discrete random variable because there are 2 outcomes (taking paracetamol or not taking paracetamol).
2. Now that we know it's discrete, we know that we have to find the probability that the exact number = 2 or written differently, P(X = 2).
3. We know that the n = 5, X = 2, and the estimated probability for people taking paracetamol is 80% or 0.80.
4. Let's add this to the equation for discrete random variables (binomial) using a TI-84 calculator:
5. 2nd -> VARS -> binompdf (trials: 5, p: 0.80, x value: 2)
6. or written: binompdf (n, p, a) ---> binompdf (5, 0.80, 2)
7. This makes the answer: 0.0512 or 5.12% that exactly 2 people will take paracetamol given this information.

**NOTE: make sure to check the assumptions for discrete random variables; we used binompdf because we were finding an exact number instead of binomialcdf if we were finding the sum of probabilities

Please let me know if this was helpful or if you need any additional support!