The annual per capita consumption of bottled water was 30.1 gallons. Assume that

Question

The annual per capita consumption of bottled water was 30.1 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 30.1 and a standard deviation of 10 gallons. a. What is the probability that someone consumed more than 30 gallons of bottled water? b. What is the probability that someone consumed between 30 and 40 gallons of bottled water? c. What is the probability that someone consumed less than 30 gallons of bottled water? d. 95% of people consumed less than how many gallons of bottled water?

Explanation / Answer

We have got params of normal distribution below.

Mean = 30.1

Stdev = 10

Using this normalize the variable:

a. P(X>30) = P(Z> (30-30.1)/10 ) = P(Z> -.01) = 1-.4960 = .5040

b. P(30<X<40) = P(X=40) - P(X=30) = P(Z = .99) - P(Z = -.01) = .8389 - .4960 = .3429

c. P(X<30) = P(Z < -.01) = .4960

d. P(Z<c) = .95

(c- 30.1)/10 = 1.645

c = 1.645*10+30.1

c= 46.55

95% of people consume less than 46.55 gallons of bottled water

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