Question

Assume that the number of sales per day of an app in the apple ios app store is normally distribbuted.

What parameters of the distribution would you need to be able to determine the probability of sales on a particular day exceeding 100 units?

If the probability of sales exceeding 100 units is 20 percent and the mean daily sales is 86 units, then what is the standard deviation of the distribution?

Answer 1

You need to know the distribution's mean and standard deviation.


`\mathbb P(X>100)=0.20\implies\mathbb P(X\le100)=0.80`

Transforming to the standard normal distribution, and letting
`\sigma` denote the standard deviation,


`\mathbb P(X\le100)=\mathbb P\left(\frac{X-86}\sigma\le\frac{100-86}\sigma\right)=0.80`

The z-score corresponding to this probability is approximately
`z=0.8416`, so you have


`\frac{100-86}\sigma=0.8416\implies\sigma=16.64`