Bottled Drinking WaterAmericans drank an average of 23.2

Step 1 of 2

(a) We gave Americans an average of 23.2 gallons of bottled water per capita in 2008.

If the standard deviation is 2.7 gallons and the variable is normally distributed, we are asked to find the probability that a randomly selected American drank more than 25 gallons of bottled water.

Let \(X\) denote the bottled water in gallons drank by Americans.

We need to find \(P(X>25)\)

We can write,

\(P(X>25)=1-P(X<25)\)

The \(z-\text { value }\) for the 25 gallons,

\(\begin{array}{l} z=\frac{X-\mu}{\sigma} \\ z=\frac{25-23.2}{2.7} \\ z=0.67 \end{array}\)

The probability value corresponding to the \(z-\text { value }\) from the standard normal table,

\(\begin{array}{l} P(Z<0.67)=0.7486 \\ P(Z>0.67)=1-P(Z<0.67)=1-0.7486=0.2514 \end{array}\)

Hence the probability that a randomly selected American drank more than 25 gallons of bottled water is 0.2514