Question 3: Recent Statistics Canada data indicate that among Canadians who do n

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Question 3: Recent Statistics Canada data indicate that among Canadians who do not develop diabetes or hypertension in their lifetimes, the average life expectancy for females is 85.5 years while the average life expectancy for males is 81.0 years. Females also outnumber males in Canada by a slim margin of 50.4% to 49.6% of the total population. Suppose we randomly select a Canadian with negligible chance of developing diabetes or hypertension (i.e. healthy diet, active, non-smoker no family history of afflictions) (a) Find a bound on the probability that this person will live to be more than 100 years old. (b) Statistics Canada also reports that the standard deviation of life expectancy in individuals who do not develop diabetes or hypertension is about 7 years for women, and about 8 years for men. Using this new information, find a better bound on the probability that our ran- domly selected individual will live to be more than 100 years old. (c) Now suppose we select 50 men at random who have a negligible chance of developing diabetes or hypertension. What is the chance that their average life expectancy will be less than 80 years? How does this compare to the chance of the same event if we were to select 50 healthy women instead?

Explanation / Answer

1)let this person be a female

for 85.5 years probability =50.4%

for 1 year -------------- = 50.4%/85.5

for 100 years------------ = 50.4%/85.5*100 = 0.589

let this person be a male

for 81.0----------- =49.6%

for 1--------- = 49.65%/81.0

for 100 y ---------- = 49.6%/81.0*100 = 0.612

average probabilty = 0.589/50.4+0.612/49.6 =0.024

2) ?w =7

?m =8

for women

z= 85.5 -100/7 =-2.07

percentage=0.0192

for men

z= 81-100/8 = -2.38

probability =0.0087

combined probability=0.0192*50.4%+0.0087*49.6%

=0.0134

3) for men

z= 81-80/8 =0.143

probability =0.45

for women

z=85.5-80/7=0.786

probability =0.218

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