Final answer:
A 95% confidence interval for the true population mean textbook weight with a sample mean of 38 ounces, population standard deviation of 6.2 ounces, and a sample size of 36 is calculated to be approximately 35.9752 to 40.0248 ounces.
Step-by-step explanation:
The subject of this question is Mathematics, and the grade level appears to be College as it deals with constructing confidence intervals, which is typically a topic covered in college-level statistics courses.
To construct a 95% confidence interval for the true population mean textbook weight when the population standard deviation is known, we use the formula for the confidence interval for a population mean, which is:
Mean ± (Z-score * (Population standard deviation/sqrt(n)))
Where:
- The sample mean is 38 ounces.
- The Z-score for a 95% confidence level is approximately 1.96.
- The population standard deviation is 6.2 ounces.
- The sample size (n) is 36.
Plugging the numbers into the formula gives:
38 ± (1.96 * (6.2/sqrt(36)))
38 ± (1.96 * 1.033)
38 ± 2.0248
The 95% confidence interval is then 35.9752 to 40.0248 ounces.