00:01
All right, so there's a insurance company table that states that men who are currently 50 years of age have an average life expectancy of 80 years, standard deviation sigma of 8.
00:15
And we're going to assume this is normally distributed, so our mean is right here in the center.
00:21
And what we want to do is find the percent of these men who would expect to die between 76 and 84 years of age.
00:30
So basically we want to find the probability that a randomly selected person dies between the age of 76 and 84.
00:38
So what does this mean in terms of our picture? so the mean is 80 right here.
00:43
So here's 76.
00:45
No, this is not to scale, this is just to give us an idea of what's happening here.
00:47
And 84.
00:50
And we want to find this area between 76 and 84.
00:57
So there's a few ways you can do it.
00:58
Here's the way i tackle this.
01:01
This is the area we're going to find, this is the percentage that we're looking for, or the proportion, and we can turn the proportion into percent.
01:11
The way i did this is i said, okay, what's the area below 76 and above 84? and then what we'll do is we'll take 1 minus the area or the probability being less than 76 plus the probability x is greater than 84.
01:33
And then that would give us our desired percentage.
01:37
So what we can do is, since it's normal, we can convert 76 and 84 into a standard normal random variable or z variable with the following transform.
01:45
X minus mu over sigma...