Answer to Question #222919 in Statistics and Probability for Mustafa Zaidi

Question

The Lakeside Coffee Shop morning customer load follows a normal distribution. The mean number of customers is 60 and the standard deviation is 15. If the store gets more than 70 customers, they need to have a fourth staff member working. What is the probability that they will need a fourth person tomorrow? Include evidence of your work by typing out your solution fully.

Answer 1

Let $X=$ the number of customers: $X\sim N(\mu, \sigma^2).$

Given $\mu=60, \sigma=15.$

$$P(X>70)=1-P(X\leq 70)$$

$$=1-P(Z\leq \dfrac{70-\mu}{\sigma})=1-P(Z\leq \dfrac{70-60}{15})$$

$$=1-P(Z\leq 0.6667)\approx0.2525$$

The probability that they will need a fourth person tomorrow is 0.2525.