00:01
So here we're talking about a normal distribution.
00:02
So the first thing that i want to do is always sketch the picture, right? here we have a mean of 12 .2, right? 12 .2 and we have sigma of 2 .8.
00:15
And for a, we are thinking about the probability that x is less than 10, right? and so we are thinking about for a, this area.
00:26
Now, the traditional way to do this is to convert to a z score, right? and use it the standardized normal distribution.
00:33
So the z score here, right, the z score is the difference from the mean converted to a number of standard deviations.
00:40
So here we have 10 minus 12 .2 over 2 .8, right? and if you convert this to a z score, right, sorry, you just do this math, you get a z score of minus 0 .7857.
00:55
And the probability that z, which is now a standard normal random variable, can be gotten from any sort of normal table, right? i think that's how you make the safest way to do this.
01:09
But also you can use, say, microsoft excel, you can use some other computer program.
01:16
And when i plug this into a calculator, i get 0 .216, right? and that looks correct, right? we knew it had to be significantly less than a half.
01:27
So for b, we have the probability that x is greater than 15.
01:35
So here i'm thinking about this area, right? 15, right? this is b...