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## Normal distribution value?

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### Normal distribution value?

A life insurance company wants to estimate their 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. By what age have 80% of the plan participants pass away?
fernand

Posts: 461
Joined: Fri Apr 01, 2011 11:35 pm

### Normal distribution value?

80% is represented by 0.8000 area under the standard normal curve
The z value which separates 0.8000 area from the rest (1.0000 - 0.8000 = 0.2000) is + 0.84 approximately
z = (X-Mean)/SD
X = Mean + (z*SD)
= 68 + (0.84*4)
= 71.36
80% of the plan participants will pass away by 71.36 years.
hymie

Posts: 98
Joined: Wed May 22, 2013 5:08 pm

### Normal distribution value?

Using a normal distribution table, you can see that .3 from the mean (meaning .5 + .3 = .8 or 80%) is .8425 standard deviation from the mean.

68 + .8425*4 = 71.37

80% are dead by the age of 71.37

This is probably the answer, considering how my work is usually impeccable.
aetos

Posts: 505
Joined: Thu Mar 31, 2011 8:43 am

### Normal distribution value?

Using a normal distribution table, you can see that .3 from the mean (meaning .5 + .3 = .8 or 80%) is .8425 standard deviation from the mean.

68 + .8425*4 = 71.37

80% are dead by the age of 71.37
hwertun52

Posts: 164
Joined: Tue Sep 18, 2012 11:19 am