Question

The average resident of Metro City produces 630 pounds of solid waste each year, and the standard deviation is approximately 70 pounds. Use Chebyshev's theorem to find the weight range that contains at least 75% of all residents' annual garbage weights.

a) Between 490 and 770 pounds
b) Between 560 and 700 pounds
c) Between 420 and 840 pounds
d) Between 350 and 910 pounds

Answer 1

To find the weight range that contains at least 75% of all residents' annual garbage weights using Chebyshev's theorem, we need to calculate the range within k standard deviations from the mean.

Step-by-step explanation:

To find the weight range that contains at least 75% of all residents' annual garbage weights using Chebyshev's theorem, we need to calculate the range within k standard deviations from the mean. In this case, we want to find the range within 75%, so k becomes 1/0.75 = 1.3333.

The range is given by:

Range = mean ± k * standard deviation

Using the given values:

Mean = 630 pounds

Standard deviation = 70 pounds

Range = 630 ± 1.3333 * 70

Range = 630 ± 93.3311

Range = (630 - 93.3311) to (630 + 93.3311)

Range = 536.6689 to 723.3311

Therefore, the weight range that contains at least 75% of all residents' annual garbage weights is between 536.6689 and 723.3311 pounds.