A drug is found... Probability question

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A drug is found to be ineffective in 5% of all cases. If 1900 patients are treated with this drug, what is the expected mean number of patients that will not respond to the drug? What is the standard deviation of this distribution? What is the probability that the drug will be ineffective for more than 105 people?
 
G'day,

This is a binomial distribution problem.

\(\displaystyle \pi \, = \, 0.05\)
n = 1900

\(\displaystyle \mu \, = \, n \pi\)

Let X be the drug is ineffective in a patient.

We want to find P(X > 105)

You'll need to apply a normal distribution approximation (because \(\displaystyle n \,pi > 5\) we can do so).

Use the mean above, and calculate the standard deviation using
\(\displaystyle \sigma = \sqrt{n \, \pi \, ( \, 1 \, - \, \pi \, ) \, }\)
to use the normal distribution to approximate P(X>105.5).

(105.5 is because we are using a continuous distribution to approximate a discrete one so a continuity correction is in order)
 
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