Question

KP Cafeteria coffee is very popular. On average, it sold 10 cups of coffee per
hour. Find the
i. probability that exactly 12 cups of coffee were sold in 2 hours,

Answer 1

Task. KP Cafeteria coffee is very popular. On average, it sold 10 cups of coffee per hour. Find the probability that exactly 12 cups of coffee were sold in 2 hours.

Solution. By assumption on average KP Cafeteria sells 10 cups of coffee per hour. Therefore it sells 20 cups per two hours.

Let $Y$ be the number of cups of coffee sold in 2 hours. Then $Y$ has Poisson distribution with $\lambda=20$. Then the probability that $Y=k$ is given by the formula:

$P(Y=k)=\frac{\lambda^{k}}{k!}\,e^{-\lambda}.$

We should compute $P(Y=12)$. Substituting values into the latter formula we get:

$P(Y=12)=\frac{20^{12}}{20!}\,e^{-20}\approx\frac{4.096*10^{15}}{2.4329*10^{18}}*2.0612*10^{-9}=3.4702*10^{15-9-18}=3.4702*10^{-12}.$