SOLUTION: Heights of women have a​ bell-shaped distribution with a mean of 163cm and a standard deviation of 8cm. Using​ Chebyshev's theorem, what do we know about the percentage

Algebra ->  Probability-and-statistics -> SOLUTION: Heights of women have a​ bell-shaped distribution with a mean of 163cm and a standard deviation of 8cm. Using​ Chebyshev's theorem, what do we know about the percentage      Log On


   

Question 1025448: Heights of women have a​ bell-shaped distribution with a mean of 163cm and a standard deviation of 8cm. Using​ Chebyshev's theorem, what do we know about the percentage of women with heights that are within 3 standard deviations of the​mean? What are the minimum and maximum heights that are within 3 standard deviations of the​ mean?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Chebyshev's theorem states that in general for any distribution,
P%28abs%28X+-+mu%29%3C=k%2Asigma%29%3E=1-1%2Fk%5E2.
==> P%28abs%28X+-+mu%29%3C=3%2Asigma%29%3E=1-1%2F3%5E2+=+1-1%2F9+=+8%2F9, or AT LEAST 88.9% are within 3 standard deviations of the mean.
abs%28X+-+163%29%3C=3%2A8+=+24 ==> -24+%3C=+X+-+163+%3C=24
==> 139+%3C=+X+%3C=+187
==> the minimum and maximum heights that are within 3 standard deviations of the​ mean are 139 and 187, respectively.