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 10 lb of paper a week? (Round your answer to one decimal place.) %

Answer 1

44.4% throw out at least 10 lb

Explanation:

Data

mean, µ = 9.4 lb

standard deviation, σ = 4.2 lb

desired point, x = 10 lb

Normal distribution formula

Z = (x - µ)/σ

This formula is used with the table attached, because in this table a mean = 0 and a standard deviation = 1 is assumed. In our case the mean and the standard deviation have other values, and the formula let us use the table. Replacing data:

Z = (x - µ)/σ

Z = (10 - 9.4)/4.2

Z = 0.1428

area below the curve = 0.056

area below the curve from -infinity to 0 = 0.5

This means that 0.5 + 0.056 = 0.556 or 55.6% of households throw out 10 lb of paper a week or less. Consequently, 100 - 55.6 = 44.4% throw out at least 10 lb

Answer 2

Answer: Pr= 42.9%

Step-by-step explanation:

SD = 4.2

Mean = 9.4

That is data are distributed between 9.4+/-4.2

Which is between 5.2 - 13.6

Probability of at least 10lb is given by;

Pr= 13.6-10 / 13.6-5.2

Pr= 3.6/ 8.4

Pr= 0.4286× 100%

Pr= 42.9%