Question

The average life of Canadian women is 73.75 years, and the standard deviation of the life expectancy of Canadian women is 6.5 years. Using Chebyshev's Theorem, determine the minimum percentage of women in Canada whose life expectancy is between 64 and 83.5 years.

Answer 1

Given that the average life of Canadian women, μ=73.75 years

Given that the standard deviation of the life expectancy of Canadian women is 6.5 years.

We have to determine the minimum percentage of women in Canada whose life expectancy is between 64 and 83.5 years.

Now, we know that k=(x-μ)/(standard deviation)

For first case, k= (83.5-73.75)/6.5= 9.75/6.5= 1.5

For second case, k= (64-73.75)/6.5= -9.75/6.5= -1.5

Thus, the difference between the mean and the given data, k=1.5 standard deviations.

From Chebyshev's theorem, the formula is

1-(1/k^2)= 1-(1/1.5^2)= 1-(1/2.25)= 1-0.4444= 0.5556

Now, converting to percentage= 0.5556*100%= 55.56%

Thus, the minimum percentage is 55.56%.