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.
