00:01
All right, so for this problem, generally speaking, we know that x is distributed as a normal random variable with a mean value of 31 and a standard deviation equal to 9.
00:14
So the way that we can do this, for each one of these, the probability of x greater than x not or probability of x less than x not, it's always going to be equal to the probability that z is greater than a particular.
00:32
Corresponding critical value, or probability that z is less than a corresponding critical value, where we know that z is equal to a particular value minus mu over sigma.
00:44
So if we have a way of finding zc, we can find x not by taking the mean value plus that critical z value times the standard deviation.
00:56
Now what i'm going to do is i'm going to be using my software here, because we're not specified how to do this, going to be using my software to find what the different critical z values are, then translating them into the x values.
01:12
Though i'll note that just based on the symmetry of the normal distribution, we have that if the probability of x greater than or equal to x not is equal to 0 .5, well, that means that x not must be at its mean value, because we should have that exactly 51 % is less than and 51 % should be greater than the mean value.
01:35
So we'd say x not is equal to 31 for part a.
01:39
Then for the remaining parts, i'm just going to put in inverse cdf, normal distribution, evaluated at some value.
01:50
I'll just call it x.
01:53
Where i'll be substituting in, basically, what i want my left tail proportions to be in each.
02:01
Case...