SOLUTION: 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. Find the minimum percentage of women in Canada w

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Question 1006314: 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. Find the minimum percentage of women in Canada whose life expectancy is between 64 and 83.5 years. Determine the upper and lower bounds on the average life expectancy of the Canadian women such that at least 90% of all population is included.
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
The limits 64-83.5 are 1.5 standard deviations from the mean.
1/1.5^2=4/9 outside maximum from Chebyshev's Inequality.
The minimum amount is 5/9 or 55.55% (repeat)
At least 90% are involved means 1/(sd)^2 must be equal to 0.10. That makes SD^2 =10 and SD=sqrt 10 or 3.16 SDs. That is 20.55 years on either side of the mean, so 90% of the population is included between 53.20 and 94.25 years.