Answer to Question #222921 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 number of customers falls below 42, then two staff members are sufficient. What are the chances only two workers are required 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 $\mu=60, \sigma=15.$

$$P(X<42)=P(Z< \dfrac{42-\mu}{\sigma})$$

$$=P(Z< \dfrac{42-60}{15})=P(Z<-1.2)$$

$$\approx0.115070$$

The probability that only two workers are required tomorrow is 0.115070.