Question

find the probability that between 1 and 4...see picture

Answer 1

Probability a Clarinex-D user has insomnia side-effect = 0.05.
The probability that between 1 and 4 patients inclusive , experienced insomnia as a side effect can be found from the binomial distribution as follows:
\[P(1\ with\ insomnia)=\left(\begin{matrix}20 \\ 1\end{matrix}\right)0.05\times 0.95^{19}=0.37735\]
\[P(2\ with\ insomnia)=\left(\begin{matrix}20 \\ 2\end{matrix}\right)0.05^{2}\times 0.95^{18}=0.18868\]
\[P(3\ with\ insomnia)=\left(\begin{matrix}20 \\ 3\end{matrix}\right)0.05^{3}\times 0.95^{17}=0.05958\]
\[P(4\ with\ insomnia)=\left(\begin{matrix}20 \\ 4\end{matrix}\right)0.05^{4}\times 0.95^{16}=0.01333\]
The required probability is found by adding P(1....) + P(2.....) + P(3......) + P(4.....)=
0.37735 + 0.18868 + 0.05958 + 0.01333 = you can calculate.