Question

Kp cafeteria is ver popular. On average, it sold 10 cups of coffee per hour. Find the probability that in an hour more than 3 cups of coffee are sold.

Answer 1

Question #8293Kp cafeteria is very popular. On average, it sold 10 cups of coffee per hour. Find the probability that in an hour more than 3 cups of coffee are sold.

Solution. The problem is weird, because the distribution of number of sold cups $N$ is not given. I believe that it has Poisson distribution with parameter 10(we all know that if $N\simeq\mathcal{P}(\lambda)$ then $EN=\lambda$, in our case $EN=10$, thus $\lambda=10$). However, this assumption is not natural, because it is stated that cafeteria is very popular, on the other hand Poisson distribution describes the occurring of rare events. We are to find $\mathsf{P}(N>3)=1-\mathsf{P}(N=0)-\mathsf{P}(N=1)-\mathsf{P}(N=2)-\mathsf{P}(N=3)\approxeq 0.99$.

Answer. $0.99$.

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