Question

The weight of topsoil sold in a week is normally distributed with a mean of 2000 tons and a standard deviation of 80 tons. (a) What percentage of weeks will sales exceed 2040 tons

Answer 1

Answer: 30.85%

Explanation:

Let x = weight of topsoil sold in a week.

Given: The weight of topsoil sold in a week is normally distributed with a mean
`(\mu)` of 2000 tons and a standard deviation
`(\sigma)` of 80 tons.

The probability that sales exceed 2040 tons =
`P(X>2040)`

`=P((X-\mu)/(\sigma)>(2040-2000)/(80))\\\\=P(Z>0.5)\\\\=1-P(Z<0.5)\\\\=1-0.6915\\\\=0.3085`

Hence, the percentage of weeks will sales exceed 2040 tons = 30.85%