Final answer:
To construct a 95% confidence interval for the population mean weight of 36 textbooks, use the formula with the given mean, population standard deviation, and Z-score for 95% confidence. The interval will be 35.98 ounces to 40.02 ounces.
Step-by-step explanation:
Based on the measurements of 36 randomly selected textbooks with a mean weight of 38 ounces and a population standard deviation of 6.2 ounces, we can construct a 95% confidence interval for the population mean weight of the textbooks. Since the population standard deviation is known, we use the normal distribution to construct this interval.
To calculate the 95% confidence interval, we need to use the formula for the confidence interval of a population mean with a known standard deviation:
Confidence Interval = Sample Mean ± (Z-score * (Population Standard Deviation / sqrt(n)))
Here, sqrt(n) stands for the square root of the sample size, and the Z-score is the value from the standard normal distribution that corresponds to the desired level of confidence. For a 95% confidence level, the Z-score is typically 1.96.
Therefore, the confidence interval for the population mean weight of the textbooks is:
38 ± (1.96 * (6.2 / sqrt(36)))
After calculating the margin of error:
38 ± (1.96 * (6.2 / 6)) = 38 ± 2.02
The 95% confidence interval is therefore 35.98 ounces to 40.02 ounces.