Answer to Question #314768 in Statistics and Probability for Jaja

Question

Each month, a Filipino household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard deviation is 2 pounds. If a household is selected at random, find the probability of its generating more than 31 pounds. (

Answer 1

We have a normal distribution, $\mu=28, \sigma=2.$

Let's convert it to the standard normal distribution,

$z=\cfrac{\bar{x}-\mu}{\sigma}$ =

$=\cfrac{31-28}{2}=1.5,$

$P(\bar{X}>31)=1-P(\bar{X}<31)=\\ =1-P(Z<1.5)=$

$=1-0.9332=0.0668$ ​(from z-table)