Question

I need help to solve this question. Please show work and also explain how to look in the standard probability table

12) A life insurance company wants to estimate its annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the participants die before they reach the age of 65?

Answer 1

z score = (x-mean)/standard deviation

When x = 65,

z = (65-68)/4 = -0.75

From z table we can see corresponding probability 0.2266

So proportion of the participants die before they reach the age of 65 = 0.2266

Note for Student

Attached is the z table where we are looking at the value marked in yellow. See corresponding z score is -0.75 (to get this z value look at the left side column where you need to navigate to -0.7 then move right side and look at the column corresponding to 0.05 and you will get 0.2266 which denotes probability corresponding to z -score -0.75)