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

(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 0.47 mgal (round to two decimal places as needed.)

Explanation:

Step1: Recall z - score formula

We use the formula $x=\mu + z\sigma$, where $x$ is the value from the original distribution, $\mu$ is the mean, $z$ is the z - score, and $\sigma$ is the standard deviation. Given $\mu = 1.68$ Mgal and $\sigma=2.9$ Mgal.

Step2: Find z - score for 80th percentile

We look up the z - score corresponding to a cumulative probability of 0.80 in the standard normal distribution table. The z - score $z_{80}\approx0.84$. Then we calculate $x$ using the formula: $x = 1.68+0.84\times2.9=1.68 + 2.436 = 4.116\approx4.12$ Mgal.

Step3: Find z - score for 29th percentile

We look up the z - score corresponding to a cumulative probability of 0.29 in the standard normal distribution table. The z - score $z_{29}\approx - 0.55$. Then we calculate $x$ using the formula: $x=1.68+( - 0.55)\times2.9=1.68-1.595 = 0.085\approx0.47$ Mgal.

Answer:

(a) 4.12 Mgal
(b) 0.47 Mgal