Question

The weekly sales of a store follow the normal distribution with a mean of 3000 euros and standard deviation 350 euros. What is the probability that the weekly sales are higher than 2800 euros?

Answer 1

$X\sim N(mean=\mu, variance=\sigma^2)$

So,

$Z=\frac{X-\mu}{\sigma } \sim N(0,1)$

Thus,

$\Phi(z)= P(Z\leq z) = \text{cdf of Z}$   ( we have to use standard normal table or software to find this value, we will use R Studio here, code: pnorm(z)

X= Weekly sales

$X\sim N(mean=3000, variance=350)$

$P(X>2800) = 1-P(X\leq 2800) \\\\ =1-P(\frac{X-3000}{350}\leq \frac{2800-3000}{350}) \\\\ =1-P(Z\leq -\frac{4}{7}) \\\\ =1-\Phi(-\frac{4}{7}) \\\\ = 1- 0.2838546 = 0.7161454$

R Studio code and output:

> pnorm(-4/7)
[1] 0.2838546