00:01
In this question, the sample size given here, let me denote by n, this is 36, and the population has the scale right, so the mean value given here 81, and the standard division which is 12 here.
00:14
So for part a, we have to describe the sampling distribution of x bar.
00:19
First of all, when we look at the sample size, 36, so this is greater than 30, so that means we can apply the central limit theorem and we can say this is approximately normal for the sample.
00:29
So the correct option for the first one which is approximately normal, this is approximately normal, is the correct answer for the part a.
00:40
But before the part b, we have to find the mean.
00:45
So the sample mean, which is denoted by, this is mu x bar, which is the same with the population mean, this is 81, and we have to find the sample standard division.
00:59
So the sample standard division denoted by sigma x bar, which is, if i apply the central limit theorem, which is the population standard division divided by the square root of the sample size, so this is 81, sorry, this is 12, and divided by the square root of 36, which is 12 over 6, which would be 2.
01:18
So i can define the random variable x bar for the sample, normally distributed, the mean is 81, and the standard division which is 2.
01:25
And for part b, so we have to find the probability of x bar, which is greater than 83 .7...