
So now, we're assuming that this sample mean is one of the 98% that falls within

2.33 standard deviations of the population mean, in this case Mu sub BT. And if

that's the case, then Mu sub BT must be, in turn, within 2.33 standard

deviations of this sample mean. So, the sample mean minus 2.33 standard

deviations, which is 1.01, will be our lower bound for this confidence interval.

So, this comes out to about 37.65, and then our upper bound for the 98%

confidence interval be 40 plus 2.33 times 1.01. So, this is 42.35 approximately.

So basically, we got the sample mean 40, and we decided that it's possible that

it's either here or here on the distribution, such that 1% of the data is either

above it or below it. Before, with the 95% confidence interval, we said most

likely it's going to be a little bit closer to the mean, so that 2.5% of the

data is above it and 2.5% is below. But now, we're being a little more lenient.

We're allowing this sample mean to be a little bit further from the population

mean. And, so now, we have a slightly bigger interval. But now, we're more sure

that the true population mean will be in this interval. Recall that before the

95% confidence interval was from 38.01 to 41.99, so it was a little smaller than

this. Good job.