Questions: The annual per capita consumption of bottled water was 31.1 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 31.1 and a standard deviation of 10 gallons. a. What is the probability that someone consumed more than 36 gallons of bottled water? b. What is the probability that someone consumed between 25 and 35 gallons of bottled water? c. What is the probability that someone consumed less than 25 gallons of bottled water? d. 95% of people consumed less than how many gallons of bottled water?

Solution Steps

To find the probability that someone consumed more than 36 gallons of bottled water, we calculate:

\[ P(X > 36) = 1 - P(X \leq 36) = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(\infty) - \Phi(0.49) = 0.3121 \]

Thus, the probability that someone consumed more than 36 gallons is:

\[ \boxed{P(X > 36) = 0.3121} \]

Next, we calculate the probability that someone consumed between 25 and 35 gallons:

\[ P(25 < X < 35) = P(X \leq 35) - P(X \leq 25) = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(0.39) - \Phi(-0.61) = 0.3808 \]

Thus, the probability that someone consumed between 25 and 35 gallons is:

\[ \boxed{P(25 < X < 35) = 0.3808} \]

Finally, we find the probability that someone consumed less than 25 gallons:

\[ P(X < 25) = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(-0.61) - \Phi(-\infty) = 0.2709 \]

Thus, the probability that someone consumed less than 25 gallons is:

\[ \boxed{P(X < 25) = 0.2709} \]

Final Answer