00:01
For this question, there is given the sample size.
00:04
So the sample size, which is denoted by n, that was given as 100, and the population mean.
00:11
So the mean value, which is denoted by mu, that was given as 29, and the standard deviation, which is denoted by sigma, that was given as 25 years.
00:22
So first of all, i have to find the first one, the sample mean and the sample standard deviation.
00:31
So first of all, the sample mean, which is equal to the population mean, and that is equal to the mu value, that was 29, and the sample standard deviation, which is the population standard division divided by square root of the sample size.
00:50
This is x bar, so this is by the way x bar, which is the population standard division was 25 and the sample mean is 100, which is equal to 25 over 10, which is 2 .5.
01:03
So we got 2 .5 here.
01:06
And what about for part b? so when we look at the sample size here, the sample size which is equal to 100, which is greater than 30.
01:16
So we can just accept, we can accept this distribution is approximately normal.
01:25
So the answer for part b, which is approximately normal.
01:29
And so i can define the random variable x bar for the sample sample, which is normal.
01:35
The normal distributed.
01:36
So the mean is 29 and the standard division is 2 .5.
01:40
So what am i supposed to get? i'm going to find the x bar which is greater than 28.
01:44
In order to get this probability, greater than or equal to.
01:48
So i'm going to use the normal cdf function here.
01:51
The normal cdf lower boundary is 28.
01:53
There is no in upper boundary.
01:55
I'm going to put a very big number.
01:56
The mean is 29 and the standard division is 2 .5 here.
02:01
Let's get the answer.
02:02
So i'm going to just press the button second and the variance.
02:05
The normal cdf, lower boundary, 28, and this is 1, and second, e99.
02:12
And the mean value is 29, and the standard division is 2 .5.
02:16
So the answer would be, this is 0 .65 and 54.
02:21
This is the answer for part c.
02:23
And what about for part d? in this case, the x bar, which is in the interval, the interval was given as 26 .8, and then 22.
02:36
1.
02:38
In order to get this probability, i'm going to again use the normal cdf function, the lower boundary, 22 .1, upper boundary, 26 .8...