EXAMPLE 4 Constructing a confidence interval for the mean of a normal population

The College Board reports that the scores on the 2014 SAT Math test were normally distributed. A sample of 25 SAT scores had a mean of . Assume that the population standard deviation of such scores is . Construct a 90% confidence interval for the population mean score on the 2014 SAT Math test.

433

image Be careful! In order to use the interval for , the population standard deviation must be known, not just the sample standard deviation. If the word problem provides the sample standard deviation but not the population standard deviation , then you cannot use the interval. You might be able to use the confidence interval for (Section 8.2).

Solution

Because the population is normal and the population standard deviation is known, the requirements for the interval are met:

We are given , , and . From Table 1, we have . Thus,

We are 90% confident that the population mean score on the 2014 Mathematics SAT test lies between 471.2 and 548.8.

NOW YOU CAN DO

Exercises 27–30.