According to botttledwater.org, in 2012, the per capita consumption of bottled w

Question

According to botttledwater.org, in 2012, the per capita consumption of bottled water in the USA was reported as 30.8 gallons. Assume the per capita consumption of bottled water in the USA is normally distributed with mean equal to 30.8 gallons and standard deviation equal to 10 gallons.

What is the probability that someone in the United States consumed more than 32 gallons of bottled water in 2012?

What is the probability that someone in the United States consumed between 10 and 20 gallons of bottled water in 2012?

Ninety nine percent (99%) of the people in the United States consumed less than how many gallons of bottled water? Round off to one decimal

Explanation / Answer

We have:

Mean = 30.80 gallons

SD = 10

Z= (X-mean)/ SD

a) What is the probability that someone in the United States consumed more than 32 gallons of bottled water in 2012?

X= 32

Z= (32-30.80)/10

Z = 0.12

We can find the value of z using normal distribution table.

For Z= 0.12, probability would be 54.78%.

b) What is the probability that someone in the United States consumed between 10 and 20 gallons of bottled water in 2012?

Z(X= 10) = (10-30.80)/10

                = -2.08

Z(X=20) = (20-30.80)/10

                = -1.08

Probability P(X=10) = 1.88%

Probability P(X=20) = 14.01%

Probability between 10 and 20 gallons = 14.01%-1.88%

                                                                  = 12.13%

c)

For probability of 99%, z value will be Z =2.33

Z= (X-mean)/ SD

2.33 = ( X – 30.80)/ 10

X= 23.30+30.80 =54.10

Hence, 99% of people consumed less than 54.10 gallons.

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