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 z - score formula

The formula for a z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. We need to find the z - score corresponding to the given percentiles from the standard normal distribution table and then solve for $x$. Given $\mu = 1.68$ Mgal and $\sigma=2.9$ Mgal.

Step2: Find z - score for the third - quartile

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

Step3: Solve for $x$

Using the z - score formula $z=\frac{x - \mu}{\sigma}$, we can re - arrange it to $x=\mu+z\sigma$. Substitute $\mu = 1.68$, $z = 0.674$, and $\sigma = 2.9$ into the formula:

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Answer:

$3.63$ Mgal