Answer to Question #298533 in Statistics and Probability for Roanne

Question

The number of patients seen in the emergency room in any hour is a random variable represented by x. Find the probability that in a given hour at least 14 patients will arrive. The probability distribution of x is: *

Answer 1

The probability distribution of $X$ is given as,

$x$   10 11 12  13 14

$p(x)$ 0.4 0.2 0.2 0.1 0.1

We determine the probability, $p(x\ge14)=1-p(p\lt 14)=1-\{p(x=10)+p(x=11)+p(x=12)+p(x=13)\}=1-(0.4+0.2+0.2+0.1)=0.1$

Therefore, the probability that in a given hour at least 14 patients will arrive is 0.1