00:02
Alrighty, we are told that we have a mean of 91 and a senior deviation of 10.
00:09
And in a normal distribution, we're approximately normal.
00:15
We want to know in part a, what's the probability of getting a value greater than 97 in this distribution? so if our mean is 91, 97 is over here to the right, and i'm finding this area over here.
00:29
So using our technology graphing calculator, normal cdf, my lower bound is 97, my upper bound is a really big number like 999 -99 -99 -9.
00:42
My mean is 91, and my standard deviation is 10.
00:46
And that gives me that that probability is 0 .2743.
00:50
Part b asked the same question, except in this case, we now have samples of size 10.
01:00
Okay, so what's going to change in that is that my standard deviation is now going to be 10 divided by the square root of 10.
01:08
So i'm still finding the same thing.
01:11
Still finding the area to the right of 97.
01:14
I'm still doing normal cdf.
01:17
I still have a lower bound of 97.
01:20
I still have an upper bound of a really big number.
01:23
I still have a mean of 91.
01:26
And again, my senior deviation is now 10 divided by the square root of 10.
01:31
Now that probability becomes 0 .0289.
01:37
Part c asked me to find the probability of getting a value greater than 97, but this time with samples of size 20.
01:47
So, yeah, my standard deviation isn't just 10.
01:49
It's going to be 10 divided by the square root of 20.
01:52
So i'm doing the same thing...