# statistics

posted by .

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 -

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.

## Similar Questions

1. ### Math

the average life expectancy in canada is 80.1 years. Estimate the country's life expectancy in hours?
2. ### Math

The average life expectancy for American men born in 1900 was 55 years. Life expectancy has increased by about .2 year for each birth year after 1900. If this trend continues, for which birth year will the average life expectancy be …
3. ### math

in 1994 the life expectancy of malews in a certain country was 70.9 years. In 1998 it was 73.6 years. Let E represent the life expectancy in year t and let t represent the number of years since 1994 The linear functionE(t) that fits …
4. ### Algebra 1A

1. b.Between the years 1975 and 2000, do women or men have the greater life expectancy?
5. ### Algebra 2

In 1950 the life expectancy of women was 72 years. In 1970 it was 75 years. E represents the life expectancy and T the number of years since 1950 (t=0 gives 1950 and t=10 gives 1960). a. fit a linear equation to predict life expectancy …
6. ### Algebra

The life expectancies for men and women in the United States can be approximated by the following formulas: Women: E= 0.126t+76.74 Men: E=0.169t+69.11 where E represents the length of life in years and t represents the year of birth,measured …
7. ### Statistics

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 …
8. ### Statistics

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 …