Question

Suppose that an actuary for an insurance company found that the life expectancy of people (living in Country A) who are currently 30 years of age is 73 years (SD = 7) for males and 77 (SD = 8) for females. What percent of current 30-year-old men and women will die before the age of 87, respectively? Provide a brief verbal description of how you obtained the answer for both males and females:

(a) For males:

(b) For females:

Thank you!

Answer 1

Suppose that an actuary for an insurance company found that the life expectancy of people (living in Country A) who are currently 30 years of age is 73 years (SD = 7) for males and 77 (SD = 8) for females. What percent of current 30-year-old men and women will die before the age of 87, respectively? Provide a brief verbal description of how you obtained the answer for both males and females:

Solution:

(a) For males:

Mean x̄ = 73

S.D, s = 7

P(x < 87) = P(x - μ /σ < 87 - 73 / 7)

P(x < 87) = P(z < 2)

P(x < 87) = 0.97725 = 97.72%

Therefore, the percent of current 30-year-old men will die before the age of 87 is 98%

(b) For females:

Mean x̄ = 77

S.D, s = 8

P(x < 87) = P(x - μ /σ < 87 - 77 / 8)

P(x < 87) = P(z < 1.25)

P(x < 87) = 0.89435 = 89.43%

Therefore, the percent of current 30-year-old women will die before the age of 87 is 89%