00:02
Hello, so this is the information we have.
00:08
Let me just underline that.
00:14
Now, let's look at a.
00:16
Let's remember that the distribution is normal because our sample size is greater than 30, and so you can use the normal distribution.
00:27
So, for the first part, we want to find the probability that the sample mean is within 12.
00:34
Or excuse me the first one is within six that's plus minus six so let's remember that this is the population mean so we want to find the probability that the sample mean is within plus minus six of that so it is that we're going to add and subtract six if we do the subtraction of six we're going to get three nine four if you do the addition we're going to get four zero six check this is the probability you want to find this is going to be 394 minus 400 oops just a second 400 divided by 60 divided by square root of 125 this is x bar minus mu over standard deviation divided by square root of n here we have 406 minus so that's the addition part we have 406 minus 400 divided by 60 divided by square root of 125.
01:57
Now, if you crank this out, we're going to have negative 1 .12.
02:06
This is the z score formula.
02:09
It's going to be positive 1 .12.
02:12
If we open this up, we're going to have probability of z less than 1 .12 minus the probability of z less than 1 .12, minus the probability of z less than.
02:23
Negative 1 .12.
02:27
Now we need the z table.
02:30
So when z is 1 .12, we're going to have 0 .86.
02:37
864.
02:39
And when z is that value, we have 0 .13 .136.
02:46
If you do the subtraction, we're going to have 0 .737 .728.
02:58
Now let's look at the b part...