00:01
All right, so we're given a random variable with a uniform, continuous uniform pdf.
00:10
F of x is a half for x being between four and six.
00:14
And we know that the expected value is five.
00:17
The variance is a third, which means the standard deviation is 0 .57735.
00:23
And we're going to do a computation using this pdf.
00:29
And specifically, we want the probability that a random sample within is 4.
00:33
49.
00:34
And the variables from this distribution will have an average value less than 4 .9.
00:39
So we want to know the probability that x bar is less than 4 .9.
00:49
So we need to find a way to use this distribution.
00:58
The fact that we have a sample size of 49 is nice because then we get to use the central limit theorem and so we're going to use the central limit theorem which says that for n for sample sizes with n greater than equal to the 30 the sampling distribution is approximately normal so that means with this sample size of 49 we can approximate this to be normal the sampling distribution to be normal which means we can convert this to a z score, which is awesome.
01:58
And so we use this formula.
02:00
Z x bar equals, and this means the z of the sampling distribution, the x bar minus the mean sampling distribution over the standard error of the sampling distribution.
02:16
But this is this is not just the same deviation here.
02:23
It's just not just that number.
02:26
It's called the standard error.
02:30
And what it actually is, is the standard deviation divided by the square root of n.
02:36
So when we compute this, what we do, so we do a little transformation here...