You measure 47 textbooks and find they have a mean weight of 50 ounces. Assume the population...

Question:

You measure 47 textbooks and find they have a mean weight of 50 ounces. Assume the population standard deviation is 10.4 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight. Give your answer as decimals, to 2 places.

Confidence Interval:

When we are given the true parameters of the population distribution, that is, the true mean and variance of the whole of the population, then we can apply the z critical value corresponding to the normal distribution for finding the confidence interval.

Answer and Explanation:

The confidence interval for the true population mean of the mean textbook weight is given by:

{eq}\mu\pm z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}\\ 50\pm z_{0.05}\frac{10.4}{\sqrt{47}}\\ 50\pm 1.645\times \frac{10.4}{\sqrt{47}}\\ (47.50, 52.50) {/eq}