# Chebyshev's theorem - standard deviation

A scientific calculator operates on the average 5.3 hour before needing a recharge. According to Chebyshev's theorem, if the operating times have a standard deviation of 0.6 hour.

A. Between what 2 values will at least 75% of the operating times fall?

B. At least what percentage of the operating times will fall in the interval from 3.5 to 7.1 hours?

#### Solution Preview

...5 TO 7.1 HOURS?

Solution:

A. We have the theorem

Chebyshev's Theorem

A mathematician named Chebyshev came up with bounds on how much of the data must lie close to the mean. In particular for any positive k, the proportion of the data that lies within k standard deviations of the mean is at least

1

1 -

k2

For example, if k = 2 this number is

...