Posted by **mzb** on Tuesday, January 22, 2013 at 6:25pm.

The average life of Canadian women is 73.75 years and the standard deviation of the women's life expectancy in Canada is 6.5 years. Using the Chebyshev's theorem, determine the minimum percentage of women in Canada whose life expectancy is between 64 and 83.5 years. Round your answer to 2 decimal places and express as a percentage (%).

- statistics -
**MathGuru**, Wednesday, January 23, 2013 at 6:27pm
Some hints:

This theorem says

1. Within two standard deviations of the mean, you will find at least 75% of the data.

2. Within three standard deviations of the mean, you will find at least 89% of the data.

Here's how the formula shows this:

Formula is 1 - (1/k^2) ---> ^2 means squared.

If k = 2 (representing two standard deviations), we have this:

1 - (1/2^2) = 1 - (1/4) = 3/4 or .75 or 75%

If k = 3 (representing three standard deviations), we have this:

1 - (1/3^2) = 1 - (1/9) = 8/9 or approximately .89 or 89%

Looking at your problem, the difference between the mean and the data given is 1.5 standard deviations.

Therefore, we have this:

1 - (1/1.5^2) = 1 - (1/2.25) = 1 - 0.44 = 0.56 = 56%

I hope this helps.

## Answer this Question

## Related Questions

- Statistics - The average life of Canadian women is 73.75 years and the standard ...
- Statistics - The average life of Canadian women is 73.75 years and the standard ...
- Algebra 2 - In 1950 the life expectancy of women was 72 years. In 1970 it was 75...
- Elementary Statistics - Heights of women have a bell-shaped distribution with a ...
- Algebra - The life expectancies for men and women in the United States can be ...
- statistics - Heights of women have a bell-shaped distribution with a mean of 158...
- Algebra 1A - 1. b.Between the years 1975 and 2000, do women or men have the ...
- Statistics - An April 15, 2002 report in Time Magazine stated that the average ...
- Statistics - An April 15, 2002 report in Time Magazine stated that the average ...
- statistics - An April 15, 2002 report in Time Magazine stated that the average ...