00:01
For this question, there is given the mean value.
00:03
So the mean, which is denoted by mu, that was given as 30 and the standard division.
00:09
So the standard deviation denoted by sigma, that was given as 8.
00:13
So in part a, what we're going to find? we're going to find if the population is normal.
00:18
So we know that the population is normal.
00:20
So i can just define the random variable x, which is normal, the distributors.
00:23
So the mean is 30 and the standard division is 8.
00:26
We need to get the probability of the values are greater than 30.
00:30
For n is equal to 4 so the n is 4 and the x value given here which is 32 so we need to get the x is greater than 32 i'm going to convert everything to the z values which is 32 minus the mean and divided by the population standard division divided by squared of the sample size which is 4 in this case so in this case the p is greater than which is 2 over this is 8 over 2 which is 4 so 2 over 4 which is 0 .5 so we need to get the probability of this one you can use table at the step or i'm going to use the graph and display, calculate your application, the normal cdf.
01:04
Lower boundary is 0 .5.
01:05
No upper boundary put some big number, the mean and the standard division.
01:09
Let me get the answer.
01:10
Press second variance, normal cdf, 0 .5, and then 1.
01:14
This is second e99.
01:16
The upper boundary is, the mean is 0, and the standard division is 1.
01:19
So the probability would be 0 .30 and 85.
01:22
This is the probability we got.
01:24
And what about for part b? so if the population distribution is positive escaped, okay, great.
01:30
What is the problem that obtaining sample mean greater than 30 to for a sample of four so in this case this is not a normal distribution and the given value n is 4 which is less than 30 so we can't apply so we can't not apply the center limit theorem here so that means we cannot find the answer because the distribution of the sample is not normal and also the sample mean the sample size is less than 30 so we can find we cannot find answer.
02:07
And what about for part c? if the population normal, okay, we know that this is normal and greater than 32 for the sample of 64, again, i'm going to follow the same process, which is greater than 32...