The annual per capita consumption of bottled water was 31.2 gallons. Assume that

Question

The annual per capita consumption of bottled water was 31.2 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 31.2 and a standard deviation of 13 gallons. a. What is the probability that someone consumed more than 31 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?

Explanation / Answer

Mean = 31.2 gallons

Standard deviation = 13 gallons

a) P(more than 31 gallons) = P(X > 31)

= 1 - P(X < 31)

= 1 - P(Z < (31 - mean)/standard deviation)

= 1 - P(Z < (31 - 31.2)/13)

= 1 - P(Z < -0.015)

= 1 - 0.4940

= 0.5060

b) P(30 < X < 40) = P(X < 40) - P(X < 30)

= P(Z < (40-31.2)/13) - P(Z < (30 - 31.2)/13)

= P(Z < 0.68) - P(Z < -0.09)

= 0.7517 - 0.4641

= 0.2876

c) P(X < 30) = 0.4641

d) Let us assumed that 90% of people consumed less than K litres

P(X < K) = 0.9

P(Z < (K - 31.2)/13) = 0.9

(K - 31.2)/13 = 1.28

K = 47.84 gallons

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