00:01
Since the amount spend on books by ces students is normally distributed, we have that the x -barrd distribution is also normally distributed with the same mean as in the population of the amount spend on books and with standard deviation equals to the standard deviation in the population divided by the square root of the sample size.
00:34
So, we want to compute a 95 confidence interval for the mean, and to do that, we can use the following formula, which is, we are going to put the sample mean here, plus and minus a z score, multiplied by the sample standard deviation estimated from the sample collected, divided by the square root of the sample size, which is 10.
01:00
The z score here is equals to 1 .96.
01:09
And we can use a z score, which is based on the standard normal distribution here, because we are assuming that the sample means coming from a normal distribution.
01:20
So we can find the z score using a z table.
01:24
And if you use a c table, you will find that the z score for a 95 % confidence interval.
01:31
Is equal to this number.
01:34
So now i just need to plug in all the values that we have in the question to compute the confidence interval that we want.
01:43
So first, the sample mean is equals to 249...