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%

Step-by-step 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 =$P(X>2040)$

$=P(\dfrac{X-\mu}{\sigma}>\dfrac{2040-2000}{80})\\\\=P(Z>0.5)\\\\=1-P(Z<0.5)\\\\=1-0.6915\\\\=0.3085$

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