### Video Transcript

A sample of the heights of 𝑛
people from a population resulted in a sample mean of 𝑋 meters. Given that the standard deviation
is known, write an interval that represents a 90 percent confidence interval for the
population mean.

For a population with an unknown
mean 𝜇 and known standard deviation, a confidence interval for the population mean,
based on a simple random sample of size 𝑛, is 𝑋 plus or minus 𝑍 times the
standard deviation over the square root of 𝑛.

And we also need to know that a 90
percent confidence interval needs a 𝑍 value of 1.645. So an interval have a lower value
and a higher value, the lowest and the highest.

So in order to find this confidence
interval for the population mean, we must take the sample mean of 𝑋 minus the 𝑍
value of 1.645 times the standard deviation over the square root of 𝑛, the
population size. And then, we take the exact same
thing, except we use addition. That will give us the highest
value.