Answer to Question #222918 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. Determine the probability that the number of customers tomorrow will be 50. Include evidence of your work by typing out your solution fully.

Answer 1

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

$$f(x, \mu, \sigma)=\dfrac{1}{\sqrt{2\pi}\sigma}e^{-(x-\mu)^2/(2\sigma^2)}, -\infin<x<\infin$$

$$P(X=50)=P(50\leq X\leq50)=\displaystyle\int_{50}^{50}f(x)dx=0$$

The probability that the number of customers tomorrow will be 50 is equal to 0.