SOLUTION: A company must decide their position on their pension plan based on the probability distribution of the length of life of their retired employees. Suppose the probability distribut

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Question 808594: A company must decide their position on their pension plan based on the probability distribution of the length of life of their retired employees. Suppose the probability distribution of the lifetimes of their employees is approximately a normal distribution with µ=74 years and σ=8.6 years.
a. What percentage of their retired employees would receive payments beyond age 76?
b. Only 12.5% of their retired employees will receive payment beyond what age?
Answer by stanbon(75887) About Me  (Show Source):
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A company must decide their position on their pension plan based on the probability distribution of the length of life of their retired employees. Suppose the probability distribution of the lifetimes of their employees is approximately a normal distribution with µ=74 years and std =8.6 years.
a. What percentage of their retired employees would receive payments beyond age 76?
z(76) = (76-74)/8.6 = 0.2326
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p(x > 76)= P(z > 0.2326) = normalcdf(0.2326,100) = 0.4081
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b. Only 12.5% of their retired employees will receive payment beyond what age?
Find the z-value with a right tail of 0.125.
invNorm(1-0.125) = 1.1503
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Find the corresponding age using x = z*s + u
age = 1.1503*8.6+74 = 83.89 years
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Cheers,
Stan H.