Answer:
Chebyshev's theorem guarantees that we will find at least approximately 89 % of the choir members between 46 and 70 inches.
Step-by-step explanation:
Chebyshev's Theorem states that, in a sample:
75% of the measures are within 2 standard deviations of the mean
89% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 58
Standard deviation = 4
Between what two heights does Chebyshev's Theorem guarantee that we will find at least approximately 89 % of the choir members?
Within 3 standard deviations the mean, so from 3 standard deviations below the mean to 3 standard deviations above the mean.
3 standard deviations below the mean
58 - 3*4 = 46
3 standard deviations above the mean
58 + 3*4 = 70
Chebyshev's theorem guarantees that we will find at least approximately 89 % of the choir members between 46 and 70 inches.
