SOLUTION: In testing a new drug, reseachers found that 5% of all patients using it will have a mild side effect. A random sample of 12 patients using the drug is selected. Find the probabili

Question 656790: In testing a new drug, reseachers found that 5% of all patients using it will have a mild side effect. A random sample of 12 patients using the drug is selected. Find the probability that:
(A) EXACTLY TWO will have this mild side effect.
(B) AT LEAST two will have this mild side effect.
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This is my work ------>
n= 12
p=0.05
mean=n*p
mean= 12*0.05
result is: mean=0.6 am I on the right track or off the tracks? with explaination so I can learn this and quit bugging you guys. Please help!!!!

Found 2 solutions by solver91311, ewatrrr:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You want the binomial distribution:

The probability of successes in trials where is the probability of success on any given trial is given by:

Where is the number of combinations of things taken at a time and is calculated by

So for the probability of exactly 2,

A little calculator work is all that is left.

At least two is a little more complicated. Here you need the sum of exactly 2 plus exactly 3 plus exactly 4...and so on. A long and tedious computation indeed. Fortunately there is a simpler method. The probablity of 0 plus P(1) plus P(2), etc., all the way up to 12 is equal to 1. So if you want the sum of P(2) plus P(3), etc. all the way to 12, calculate P(0) plus P(1) and subtract from 1.

So you need to punch:

Into your calculator and then subtract the result from 1. Still ugly, but not so bad a mother couldn't love it.

John

My calculator said it, I believe it, that settles it

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

Hi,
Re: TY, w/o capability of using Your own calculator, the only option would be using an on-line site like the following,
which is relatively uncomplicated calculator to enter the information given:
http://stattrek.com/online-calculator/binomial.aspx
P(x = 2) = .0988 (rounding to 4 decimal places)
P(x≥ 2) = .1184
Important thing to understand is with only 5% having a mild side effct...
Probability of even 2 out of 12 people having a side effect is very small.
This is a case of Bionomial Probability Distribution
Note: The probability of x successes in n trials is:
P = nCx* where p and q are the probabilities of success and failure respectively.
this case p = .05 & q = .95 and n = 12
nCx =
P(x = 2) = 12C2(.05)^2(.95)^10 0r binompdf(12,.05,2) using TI83
P(x ≥ 2) = 1- P(x <2) = 1-P(0) - P(1)
0r 1 - binomcdf(12,.05,1) using TI83
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