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 12 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. 97.5​% of people consumed less than how many gallons of bottled​ water?

Answer 1

Solution:

We are given:

Let x be the number of gallons of bottled water someone consumes.

a. What is the probability that someone consumed more than 36 gallons of bottled water?

Answer: We have to find

Using the z-score formula we have:

  

Now using the standard normal table, we have:

Therefore, the probability that someone consumed more than 36 gallons of bottled water is 0.3446

b. What is the probability that someone consumed between 25 and 35 gallons of bottled water?

Answer: We have to find

Using the z-score formula we have:

Now using the standard normal table, we have:

Therefore, the probability that someone consumed between 25 and 35 gallons of bottled water is 0.3240

c. What is the probability that someone consumed less than 25 gallons of bottled water?

Answer: We have to find

Using the z-score formula we have:

  

Now using the standard normal table, we have:

d. 97.5 % of people consumed less than how many gallons of bottled water?

Answer: We have to find the z value corresponding to the area 0.975. Using the standard normal table, we have:

Using the z-score formula, we have:

Therefore, 97.5% of people consumed less than 54.72 gallons of bottled water.