www.helpyourmath.com is an OER website to help students to save money on textbooks and homework systems. A survey of 30 randomly selected students finds that they save a mean of $\$ 134$ per semester by using www.helpyourmath.com. Assume the date comes from a normal distribution and the sample standard deviation is $\$ 20$ per month.

Confidence Interval: What is the $90 \%$ confidence interval to estimate the population mean? Round your answers to two decimal places.

Step 1 ：Given values are: sample mean = \$134, sample standard deviation = \$20, sample size = 30, and z-score = 1.645 for a 90% confidence level.

Step 2 ：First, calculate the standard error, which is the standard deviation divided by the square root of the sample size. The formula for standard error is \( \frac{Standard Deviation}{\sqrt{Sample Size}} \).

Step 3 ：Substitute the given values into the formula: \( \frac{20}{\sqrt{30}} \) which gives a standard error of approximately 3.65.

Step 4 ：Next, calculate the margin of error by multiplying the standard error by the z-score. The formula for margin of error is \( Z-Score \times Standard Error \).

Step 5 ：Substitute the given values into the formula: \( 1.645 \times 3.65 \) which gives a margin of error of approximately 6.01.

Step 6 ：Finally, calculate the confidence interval by adding and subtracting the margin of error from the sample mean. The formula for confidence interval is \( (Sample Mean - Margin of Error, Sample Mean + Margin of Error) \).

Step 7 ：Substitute the given values into the formula: \( (134 - 6.01, 134 + 6.01) \) which gives a confidence interval of approximately (\$127.99, \$140.01).

Step 8 ：Final Answer: The 90% confidence interval to estimate the population mean is approximately \(\boxed{(\$127.99, \$140.01)}\).