Answer to Question #326328 in Statistics and Probability for VITHU

Question

The quantity produced daily at the ABC cement factory is approximately normally

distributed with mean 0.82 and standard deviation 0.14. The units are on millions of tons.

Find the probability that the total production will between 0.80 and 0.85 million tons.

Answer 1

We have a normal distribution, $\mu=0.82, \sigma=0.14.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}.$

$z_1=\cfrac{0.80-0.82}{0.14}=-0.14;\\ z_2=\cfrac{0.85-0.80}{0.14}=0.36;\\ P(0.80<X<0.85)=P(-0.14<Z<0.36)=\\ =P(Z<0.36)-P(Z<-0.14)=\\ =0.6406-0.4443=0.1963 \text{ (from z-table).}$