Question

a water footprint is a measure of the appropriation of fresh water. the per capita water footprint (in mega gallons) in a certain country for a recent year can be approximated by a normal distribution, as shown in the figure. (a) what water footprint represents the 80th percentile? (b) what water footprint represents the 29th percentile? (c) what water footprint represents the third quartile? (a) the water footprint that represents the 80th percentile is 4.12 mgal (round to two decimal places as needed.) (b) the water footprint that represents the 29th percentile is 0.09 mgal (round to two decimal places as needed.) (c) the water footprint that represents the third quartile is mgal (round to two decimal places as needed.)

Explanation:

Step1: Recall the z - score formula

The formula for a value \(x\) in a normal distribution is \(x=\mu + z\sigma\), where \(\mu\) is the mean, \(\sigma\) is the standard deviation, and \(z\) is the z - score corresponding to the given percentile. We know that \(\mu = 1.68\) Mgal and \(\sigma=2.9\) Mgal.

Step2: Find the z - score for the third - quartile

The third - quartile represents the 75th percentile. Looking up the z - score in the standard normal distribution table, the z - score \(z\) corresponding to the 75th percentile is approximately \(z = 0.674\).

Step3: Calculate the water footprint

Substitute \(\mu = 1.68\), \(z = 0.674\), and \(\sigma = 2.9\) into the formula \(x=\mu+z\sigma\).

$$x=1.68+0.674\times2.9$$

$$x = 1.68+1.9546$$

$$x=3.6346\approx3.63$$

Mgal

Answer:

3.63 Mgal