Question

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?

Answer 1

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