00:01
Okay, so we have this test that has a mean of 74 and a standard deviation of 6 .8 and follows a normal distribution.
00:08
So first we want to know if a student is selected at random, here i'm going to draw the normal curve first, has a mean of 74.
00:19
There we go.
00:20
Okay, so we want to see if a student is selected at random, what's the probability that his test is less than 65? so 65 is about right hereish on the curve.
00:34
We're looking for this probability here.
00:37
Right, so i'll compute a z score for 65.
00:43
Z is x minus mu over sigma.
00:46
So that will be 65 minus the mean over 6 .8.
00:52
That gives us a z score.
00:54
Okay, so we have this test that has a mean of 70, of negative 1 .32 approximately so i am going to then look up negative 1 .32 on the z table and that should give me the area below there what i'm looking for so that gives me 0 .0934 here so that is the probability that a test is less than 65 for for b we say what about a random sample of n equals 50 students what's the probability that their test score is greater than 75 so now the z formula that we're going to use is going to be different because we're talking about a mean so we're going to use x bar minus mu over sigma over the square root of n because we have to take into account that sample size so the x bar that i'm looking for is that i'm looking for greater than 75 right the mean is still 74 divided by 6 .8 over the square root of 50.
02:10
So that new z score comes out to...
02:14
Okay, so we have this test that has a mean of 74, 1 .04 approximately.
02:22
So when i look up that z score on the normal curve, i get...
02:33
Okay, so it's about one centered deviation above the main, right? like right here.
02:37
I'm looking for this area.
02:38
When i look up 1 .04 on the curve, curve, i get .8508, but i have to remember that's the area below that point...