00:01
There is a normal distribution given in this question.
00:03
So the mean value was given here, which is denoted by mu, that is 45, and the standard deviation, denoted by sigma, and that was given as 4 here.
00:16
So i can define the random variable x, which is normally distributed.
00:20
This is 45 and 4.
00:22
And the next step, which is, so the sample size was given here, which is there are taken 10 doctors.
00:30
So the sample size is 10 here.
00:33
So what we need? we need the sample standard division.
00:36
So i'm going to apply the central limit theory, which is the population standard division divided by square of the sample size.
00:43
This is sigma x bar.
00:45
So this is 4 divided by square root of 10.
00:48
And i can define the random, the x bar as a random variable for the sample, which is normally distributed.
00:54
So the mean is the same with the population.
00:56
And the standard division, 4 divided by square width of, 10 here.
01:02
So in the first part of the question, we need to find the x bar, which is less than 43 .80.
01:10
To get this probability, i'm going to use the normal cdf function of the graphing display calculator.
01:15
There is no lower boundary, put some very small number...