00:01
For this question, the population mean denoted by mu, which is given as 85, and the population standard deviation, which is given as 7 here, and the sample size, which is 49.
00:11
So, part a, we have to just describe the sampling distribution of x bar.
00:17
First of all, when we look at the sample size, which is greater than 39, the 49 is greater than 39, so that means we can use a normal approximation to just get this question.
00:28
So, this is a standard distribution for the sample mean.
00:31
So, what do i need? i need the sample mean, which is the same with the population mean, and also i need the sample standard deviation.
00:40
To get the sample standard deviation, i'm going to divide the population standard deviation by the square root of the sample size.
00:45
So, from here, i can just denote by sigma x bar, which is 7 over square root of 49, which is 1.
00:52
So, i can define the random variable x bar for the sample.
00:55
This is normally distributed.
00:56
The mean is 85, and the standard deviation 1.
01:00
So, in the first, in the part b, we have to find the random variable x bar, which is greater than 86 .55.
01:07
To get this probability, i'm going to use the graphing display calculator application, normal cdf, lower boundary 86 .55.
01:15
There is not an upper boundary, put a very big number, so the mean and the standard deviation.
01:20
Press second, variance, normal cdf, lower boundary 86 .55...