Question

The daily sales of Burger Baby restaurants follow the normal distribution with a standard deviation of $4000. What is the probability that the average sales are really $36,000 or less per day? Assume the actual population average is $40,000 per day.

Answer 1

Denote by $\xi$ a random variable corresponding to average sales. $\xi$ has normal distribution with mean $\mu = 40000$ and standard deviation $\sigma = 4000$.

$$\xi \sim N(\mu, \sigma^2)$$

Then

$$P(\xi \leq 36000) = \Phi\left(\frac{36000 - 40000}{4000}\right) = \Phi(-1) = 0.1587$$

Thus the probability that average sales are 36000 or less per day is equal to 0.1587.