Question

Bottled Drinking Water Americans drank an average of 23.2 gallons of bottled water per capita in 2004. If the standard deviation is 2.7 gallonvariable is normally distributed, find the following probabilities. Use a graphing calculator and round the answers to four decimal places.Between 16 and 26 gallons of bottled water.P (between 16 and 26 gallons of bottled water)

Answer 1

We need to find

P ( 16 < x < 26) =

In order to solve this, we need to use the following formula

$z=\frac{x-\mu}{\sigma}$

where:

mean: μ = 23.2

standard deviation: σ = 2.7

x1 = 16

x2 = 26

z is the z-score

First, we need to calculate the Z-score when x = 16 and x = 26 , then we find the probability using a z-table

$z_{16}=\frac{16-23.2}{2.7}=-2.666$$z_{26}=\frac{26-23.2}{2.7}=1.037$

using the values above, we use the z-table and find the probability P (16[tex]\begin{gathered} P(x=16)=0.0038311 \\ P(x=26)=0.85013 \\ P(16Thus, P = 0.8463