00:01
In the ask question, a population has a standard deviation of 16 if a sample of size 64 is selected from this population.
00:13
It's required to find the priority that the sample mean will be within plus or minus 2 of the population mean.
00:27
Then it is between mu minus 2 and mu plus 2.
00:36
Let's see how we can calculate this probability.
00:38
If we could from the center limit theorem we know that as long as sample size is sufficiently large significantly larger 30 the sample mean has a distribution that follows a normal distribution with mean equals the same mean of the population and standard deviation the same as the population divided by a square root of n this is the mean of x bar and this is standard division of the distribution of x bar.
01:30
Now we have known that x bar follows a normal distribution then we can standardize here.
01:37
We can say that this probability is equivalent to the probability of z to be between the z scores of mu minus 2 and mu plus 2.
01:47
Now we can find the 0 score, we get the row score, then we subtract the mean, then divided divide by the standard deviation we get the score subtract the mean divide by the standard deviation then this is the probability of z to be between minus 2 divided by 16 divided by 4 sorry divided by 8 the square root of 64 is 8 and here it's 2 divided by 16 by 8 it is the probability of z to be between minus 1 and 1 this is the probability or the percentage of values that lies within one standard deviation from the mean for a normal distribution or sun normal distribution when you that this equals about 68 % from the empirical rule and choose the correct answer from the choices it's about 0 .6 -826.
03:20
We choose a.
03:23
Of course, the probability can't be negative.
03:28
We choose a...