# Discrete probability distribution problem

• Oct 1st 2013, 03:39 AM
Nora314
Discrete probability distribution problem
Hi!

The problem:

Cecile is a nurse and has a 0,25 of working a night shift. In the latest time period there have been 10 cases of death at night time by the nursing home,and a remarkably large number of these have happened while Cecilie has been on duty. 7 of the cases of death have been on her duty. Therefore, an investigation has been started to find out if she has anything to do with these deaths.
Assume in the following that all the deaths are natural and that they have happened at
di erent nights.

Let X be a stochastic variable that describes the number out of n = 10 natural deaths that
happen on Cecilie's night shifts.

What is the probability of 7 or more deaths, out of the 10 deaths at night time, happening while Cecilie is on duty?

The right answer should be: 0,004

I am not sure how to calculate this, I tried finding the chance of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 deaths happening while she is on duty, but I am not sure how to find the chance of it being 7 or more.

I would really appreciate any feedback, thank you!
• Oct 1st 2013, 04:22 AM
Plato
Re: Discrete probability distribution problem
Quote:

Originally Posted by Nora314
The problem:

Cecile is a nurse and has a 0,25 of working a night shift. In the latest time period there have been 10 cases of death at night time by the nursing home,and a remarkably large number of these have happened while Cecilie has been on duty. 7 of the cases of death have been on her duty. Therefore, an investigation has been started to find out if she has anything to do with these deaths.
Assume in the following that all the deaths are natural and that they have happened at
dierent nights.
The right answer should be: 0,004

You can see the calculation here.
• Oct 1st 2013, 04:34 AM
Nora314
Re: Discrete probability distribution problem
Wow, thank you so much! I really appreciate it! I hope you have a good day.
• Oct 2nd 2013, 12:06 AM
Nora314
Re: Discrete probability distribution problem
I was wondering if you could help me with a futher part of the question:

Lets assume that about 300 other nurses have the same sort of position as Cecilie, in
nursing homes around Norway. What is the probability of at least one of these 300
nurses having 7 or more out of 10 natural deaths happening while they are on duty?

Does the answers in this subsection give any reason to strengthen the suspicion towards