Final answer:
The 99% confidence interval for the true population mean textbook weight is approximately (46.14 ounces, 57.86 ounces), calculated using a sample mean of 52 ounces, a population standard deviation of 14.8 ounces, and a sample size of 42.
Step-by-step explanation:
To construct a 99% confidence interval for the true population mean textbook weight, we'll use the formula for a confidence interval when the population standard deviation is known:
Confidence interval = ×-bar ± (Z* × (σ/√n))
Where ×-bar is the sample mean, Z* is the Z-value that corresponds to the chosen confidence level, σ is the population standard deviation, and n is the sample size. Here, ×-bar is 52 ounces, σ is 14.8 ounces, and n is 42.
We'll obtain the Z-value for 99% confidence from a standard normal distribution table or calculator, which is approximately 2.576. Plugging in the values, we get the following:
Confidence interval = 52 ± (2.576 × (14.8/√42))
Now we calculate the margin of error:
Margin of error = 2.576 × (14.8/√42) ≈ 5.857 ounces
Finally, we find the confidence interval:
Confidence interval = (52 - 5.857, 52 + 5.857)
Confidence interval = (46.143, 57.857)
Therefore, the 99% confidence interval for the mean weight of the textbooks is approximately (46.14 ounces, 57.86 ounces).