Question

Each month, an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard deviation is 2 pounds. If the data conforms to a normal distribution and a household is selected at random, the probability of its generating between 28 and 30 pounds per month is about __?

Answer 1

Answer: 0.3413

Step-by-step explanation:

Given: an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard deviation is 2 pounds.

Let $\mu=\text{ 28 pounds and }\sigma=\text{ 2 pounds}$ .

Let x be the random variable that denotes the amount of newspaper for garbage generated by each household each month.

If the data conforms to a normal distribution and a household is selected at random, the probability of its generating between 28 and 30 pounds per month is about

$P(28<x<30)=P(\dfrac{28-28}{2}<\dfrac{x-\mu}{\sigma}<\dfrac{30-28}{2})\\\\=P(0<z<1)\ \ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\ =P(z<1)-P(z<0)\\\\=0.8413-0.5=0.3413$

Hence, the required probability is 0.3413.