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# Confidence Intervals: Women Height, Package Weights

(23) Assume that the heights of women are normally distributed. A random sample of 20 women have a mean height of 62.5 inches and a standard deviation of 2.3 inches. Use the Chi-Square distribution to construct the 99% confidence interval for the population standard deviation a of women's heights.

(24) FedEx Ground would like to estimate the mean weight of all packages shipped from their Moon Township Facility. They took the following random sample of the weights of 36 packages shipped from this facility:
12.0, 9.2, 9.0,13.0, 4.6, 11.7, 8.2, 9.5, 8.6, 21.9, 30.0, 17.6, 14.0, 19.2, 17.0, 11.0, 9.0, 10.9, 8.3, 7.6, 14.7, 24.5, 23.1, 7.0, 6.7, 9.3, 16.1, 5.4, 6.9, 7.5, 15.2, 10.0, 3.0, 9.6, 11.2,
9.5.
Find the 90%, 95% and 99% confidence intervals for the mean weight of all packages shipped by FedEx Ground from the Moon Township Facility.

Decide whether the normal or the t-distribution applies.
You will need to find the sample mean and sample standard deviation first.

#### Solution Preview

(23) Assume that the heights of women are normally distributed. A random sample of 20 women have a mean height of 62.5 inches and a standard deviation of 2.3 inches. Use the Chi-Square distribution to construct the 99% confidence interval for the population standard deviation a of women's heights.

Solution:

The 99% confidence interval for population standard deviation is

(ns^2 / χ2 0.005 < σ < ns^2 /χ2 0.995

since the population ...

#### Solution Summary

Calculates specified confidence intervals, complete with formula and calculations.

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