00:01
Okay, so we've been told that the average cost of a car repair is 367, some unit of currency, or no pounds, dollars, whatever you like, and that the standard deviation is 88.
00:14
So that's what i've written down here.
00:16
And then we're asked some questions.
00:17
So we're asked, what's the probability that the cost of an individual repair is bigger than 450 if this data is normally distributed? so we're just going to use as it values.
00:28
So part a, the probability that c, the cost, i'm using c for the cost, is bigger than 450, is the probability that z is bigger than 450 minus 367 divided by 88.
00:47
This is using our classic z equals x bar minus mu over sigma.
00:56
And this is the probability that z is greater than 0 .943.
01:06
Now the probability that z is greater than 0 .943 is this probability here.
01:17
But in our tables we're always given the probability of z being less than some value.
01:22
And we can see that this probability is just going to be one minus the probability of being, of z being less than the same value.
01:31
And this is 1 minus 0 .8264, if you use your z table and look at 0 .94, which is 0 .1736.
01:48
Part b then is very similar.
01:50
We want c being less than 250 this time.
01:53
So we basically do the same thing.
01:55
This is the same as probability of z being less than 250 minus 367.
02:01
Over 88, which is the probability of z being less than minus 1 .33.
02:13
Again, that's going to be this probability here.
02:20
But because of the symmetry of the normal distribution, that's the same as this section here.
02:25
And so we can see that this is just going to be equal to 1 minus probability that z is less than the positive 1 .33...