Answer
a) 0.22
b)0.028
c) 0.25
Work Step by Step
Let $X$ be the random variable of number of patients that leave without being seen by a physician in the hospital 4 . $X$ has the binomial distribution with parameters $n=5, p$ Calculate the parameter $p$ directly from the table given in the example $2-8:$
$$
p=\frac{242}{4329}=0.0559
$$
The probability mass function of $X$ is given by:
$$
\mathbb{P}(X=x)=\left(\begin{array}{l}
5 \\
x
\end{array}\right) p^{x} \times(1-p)^{5-x}, x=0,1, \ldots, 5
$$
Calculate using this formula:
$$
\begin{array}{l}
\mathbb{P}(X=1)=0.22 \\
\mathbb{P}(X \geq 2)=1-\mathbb{P}(X=0)-\mathbb{P}(X=1)=0.028 \\
\mathbb{P}(X \geq 1)=1-\mathbb{P}(X=0)=0.25
\end{array}
$$
