The annual per capita consumption of bottled water was 34.8 gallons.Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 34.8 and a standard deviation of 12 gallons. a.What is the probability that someone consumed more than 35 gallons of bottled water? b.What is the probability that someone consumed between 20 and 30 gallons of bottled water? c.What is the probability that someone consumed less than 20 gallons of bottled water? d.90%of people consumed less than how many gallons of bottled water?Round to four decimal places as​ needed.)

Sure, I can do that. Here are the answers to your questions:

a. To find the probability that someone consumed more than 35 gallons of bottled water, we first need to calculate the z-score. The z-score is calculated as (X - μ) / σ, where X is the value we're interested in, μ is the mean, and σ is the standard deviation. So, the z-score for 35 gallons is (35 - 34.8) / 12 = 0.0167. Looking this up in a standard normal distribution table, we find that the probability associated with this z-score is 0.5069. However, since we're interested in the probability of consuming more than 35 gallons, we need to subtract this from 1 (since the total probability under the curve is 1). So, the probability of consuming more than 35 gallons is 1 - 0.5069 = 0.4931 or 49.31%.

b. To find the probability that someone consumed between 20 and 30 gallons of bottled water, we need to calculate the z-scores for both 20 and 30 gallons and find the area between them under the curve. The z-score for 20 gallons is (20 - 34.8) / 12 = -1.2333 and for 30 gallons is (30 - 34.8) / 12 = -0.4. Looking these up in a standard normal distribution table, we find that the probabilities associated with these z-scores are 0.1085 and 0.3446 respectively. So, the probability of consuming between 20 and 30 gallons is 0.3446 - 0.1085 = 0.2361 or 23.61%.

c. To find the probability that someone consumed less than 20 gallons of bottled water, we use the z-score for 20 gallons that we calculated in part b. Since we're interested in the probability of consuming less than 20 gallons, we can use the probability associated with the z-score directly. So, the probability of consuming less than 20 gallons is 0.1085 or 10.85%.

d. To find the number of gallons that 90% of people consumed less than, we need to find the z-score associated with a cumulative probability of 0.9. Looking this up in a standard normal distribution table, we find that the z-score is approximately 1.2816. We can then use this z-score to find the corresponding value of X using the formula X = μ + zσ. So, X = 34.8 + 1.2816 * 12 = 49.1372. So, 90% of people consumed less than approximately 49.1372 gallons of bottled water.