Question

The "Garbage Project" at the University of Arizona reports that the amount of paper discarded by households per week is normally distributed with mean 9.4 lb and standard deviation 4.2 lb. What percentage of households throw out at least 7 lb of paper a week?

Answer 1

Answer:

The answer is 71.61%.

Step-by-step explanation:

Households discarding paper week is given to be normally distributed with a mean, $\mu$ = 9.4 lb.

The normally distributed distribution has a standard deviation given as $\sigma$ = 4.2 lb.

The proportion of households that throw out at least 7 lb of paper a week is to be found.

Therefore we have to find p(X ≥ 7) which can be written as

   p(X ≥ 7)  = 1 - p(X < 7)

                  = 1 - p( Z < $\frac{x - \mu}{\sigma}$ )

                 =  1  - p( Z < $\frac{(7 - 9.4)}{4.2}$ )

                 = 1 - p( Z < -0.571 )

                 = 1 - 0.2839

                 = 0.7161

Therefore the percentage of households that throw out at least 7 lb paper a week is 71.61%