Question

Heights of women have a​ bell-shaped distribution with a mean of 161 cm and a standard deviation of 5 cm. Using​ Chebyshev's theorem, what do we know about the percentage of women with heights that are within 2 standard deviations of the​ mean? What are the minimum and maximum heights that are within 2 standard deviations of the​ mean? At least ___% of women have heights within 2 standard deviations of 161 cm. ​(Round to the nearest percent as​ needed.)

Answer 1

Solution:

At least (1-(1/2)^2)% = 75% of the data is within 2 std
of the mean

What are the minimum and maximum heights that are within 5 standard deviations of the​ mean?
Minimum:: 161-2*5 = 151 cm
Max:: 161 + 2*5 = 171 cm

At least 75​% of women have heights within 2 standard deviations of 161 cm.

The minimum height that is within 2 standard deviations of the mean is
151 cm.
The maximum height that is within 2 standard deviations of the mean is
171 cm.