00:01
In this exercise, we are told that the number of facebook friends, we will call that random variable x, is normally distributed with a mean of 230 friends and a variance of 7 ,225.
00:14
And then we are asked that for a sample of 60 facebook users, what is the probability that the sample average is greater than 210? so this is what is the probability sample average is greater than 210? and to answer this question, we have to know how sample averages are distributed.
00:41
Now, since x is normally distributed, samples from x or the averages of samples from x are also normally distributed.
00:56
So we can say that sample averages are normally distributed, and we can also say that the mean of sample averages is equal to the mean of the population, which is 230.
01:08
And the standard deviation of sample averages is equal to the standard deviation of the population divided by the square root of the sample size.
01:24
Now we have the variance of the population.
01:29
Standard deviation is going to be the square root of the variance, which is 85.
01:40
So this quotient becomes 85 divided by the square root of 60, which is 10 .9735.
01:52
So here we have completely defined the distribution of sample averages.
02:05
So now we can make the calculation.
02:08
We can say that this is equal to 1 minus the probability that the sample average is at most 210...