00:01
A normal distribution is given here in this question and let me take some notes.
00:07
The mean, which is denoted by the symbol mu, that is 190 millimeter.
00:16
And the standard deviation, which is denoted by sigma, that is 7 .4.
00:22
So suppose that 44 individuals are randomly chosen.
00:27
So that means the sample size is 44.
00:30
So let's say n is 44.
00:33
So in part a, we have to find the distribution of the mean and the standard deviation.
00:41
So the distribution mean, let's say this is x bar.
00:47
This is a mean of sample, which is also equal to the mean of population.
00:55
So the mean of the population, we know that that is 190.
00:58
So the mean of the sample or sample mean is equal to 190, which is.
01:02
Same with the population mean.
01:05
And what about for the sample standard division? so the sample standard deviation, standard deviation has the formula, which is the population standard division divided by squared of the sample size here.
01:20
So the population standard division, let's denote by this symbol here.
01:26
That is 7 .4 divided by square root of 44.
01:31
Let's get the answer.
01:32
This is a 7 .4 divided by squared of 44 which give us the value of 1.
01:42
This is 1 point let's say this is 1 .12.
01:47
1 .12 is the new standard deviation for this one so we can just define the random variable x bar which is normally distributed the mean value is 190 and the standard division is 1 .12.
02:00
And let's take a look at part b.
02:03
For the group of 44, find a probable that the average hand length is more than this one...