High School

The mean weight of males is 150 lbs with a standard deviation of 15 lbs. Use Chebyshev's rule.

a. At least 55% of males weigh between 135 lbs and 165 lbs.

b. At least 75% of males weigh between 135 lbs and 165 lbs.

c. At least 80% of males weigh between 120 lbs and 180 lbs.

d. At least 90% of males weigh between 120 lbs and 180 lbs.

Answer :

Final answer:

Using Chebyshev's rule, we can determine the percentage of data within a certain range from the mean. At least 55%, 75%, 80% and 90% of males weigh between certain weight ranges based on the given mean and standard deviation.

Explanation:

To use Chebyshev's rule, we can calculate the range within which a certain percentage of data lies from the mean, given the standard deviation. Chebyshev's theorem states that for any number k greater than 1, at least 1 - 1/k^2 of the data lies within k standard deviations of the mean.

a. Here, k = 165-150/15 = 1, which means 100% lies within 1 standard deviation of the mean. So at least 55% lies between 135 lbs and 165 lbs.

b. Since k = 165-150/15 = 1, at least 100 - 1/1^2 = 100% - 1% = 99% lies within 2 standard deviations. So at least 75% lies between 135 lbs and 165 lbs.

c. k = 180-150/15 = 2, so at least 100 - 1/2^2 = 100% - 1/4 = 100% - 25% = 75% lies within 2 standard deviations. So this statement is true.

d. k = 180-150/15 = 2, so at least 100 - 1/2^2 = 100% - 1/4 = 100% - 25% = 75% lies within 2 standard deviations. So this statement is true as well.