Question

In: Statistics and Probability

The annual per capita consumption of bottled water was 31.5 gallons. Assume that the per capita...

The annual per capita consumption of bottled water was 31.5 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 31.5 and a standard deviation of 12 gallons.

a. What is the probability that someone consumed more than 37 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. 90​% of people consumed less than how many gallons of bottled​ water?

Solutions

Expert Solution

Given that, mean = 31.5 gallons and

standard deviation = 12 gallons

a) We want to find, P(X > 37)

The probability that someone consumed more than 37 gallons of bottled​ water is 0.3228

b) We want to find, P(30 < X < 40)

The probability that someone consumed between 30 and 40 gallons of bottled​ water is 0.3128

c) We want to find, P(X < 30)

The probability that someone consumed less than 30 gallons of bottled​ water is 0.4483

d) We want to find, the value of x such that, P(X < x) = 0.90

Answer : 46.86 gallons


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