The mean of a distribution is 20 and the standard deviation is 2. Use Chebyshev\

Question

The mean of a distribution is 20 and the standard deviation is 2. Use Chebyshev's theorem. a. At least what percentage of the values will fall between 10 and 30? b. At least what percentage of the values will fall between 12 and 28? In a distribution of 160 values with a mean of 72, at least 120 fall within the interval 67-77. Approximately what percentage of values should fall in the interval 62-82? Use Chebyshev's theorem. Calories The average number of calories in a regular-size bagel is 240. If the standard deviation is 38 calories, find the range in which at least 75% of the data will lie. Use Chebyshev's theorem. Time Spent Online Americans spend an average of 3 hours per day online. If the standard deviation is 32 minutes, find the range in which at least 88.89% of the data will lie. Use Chebyshev's theorem.

Explanation / Answer

32.

Mean = 20
Stdev = 2

a. the 2 values are 5 standard deviation away, So Chebeshev' theorm says:

= 1-1/2^5
=.96875

b. The same with 4 standard deviation away:
=1-1/2^4
=.9375

35. Chebyshev's theorem states that within any range, at least 88.89% of the values fall within three standard deviations from the mean.  

.8889 = 1-1/3^2 = 8/9

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