Question

A local electrical appliances shop has found from the experience that the demand of the tube lights is distributed as Poison with mean of 4 tube lights per week. If the shop keep 6 tubes during a particular week, what is the probability that the demand will exceed the supply during that week.

Answer 1

Let $X=$ the demand of the tube lights: $X\sim Po(\lambda).$

$$P(X=x)=\dfrac{e^{-\lambda}\cdot\lambda^x}{x!}$$

Given $\lambda=4$

$$P(X>6)=1-P(X\leq6)$$

$$=1-0.88933=0.11067$$

The probability that the demand will exceed the supply during that week is 0.11067.