Question

Suppose the age at death for politicians can be modeled by an approximately normal distribution with a mean of 72.9 years and a standard deviation of 7.2 years. (Use a table or technology.)

Calculate the z-score representing the longest 25% of life expectancies for politicians. (Round your answer to two decimal places.)

Calculate the value (in years) representing the top 25% of life expectancies. (Round your answer to one decimal place.)

yr

Answer 1

Given that,

mean = $\mu$ = 72.9

standard deviation = $\sigma$ =7.2

Using standard normal table,

P(Z > z) = 25%

= 1 - P(Z < z) = 0.25

= P(Z < z ) = 1 - 0.25

= P(Z < z ) = 0.75

z = 0.67 (using standard normal (Z) table )

Using z-score formula  

x = z * $\sigma$ + $\mu$

x= 0.67*7.2+72.9

x= 77.7 years