Question

The annual per capita consumption of bottled water was 34.734.7 gallons. assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 34.734.7 and a standard deviation of 1313 gallons.
a. what is the probability that someone consumed more than 3535 gallons of bottled​ water?
b. what is the probability that someone consumed between 3030 and 4040 gallons of bottled​ water?
c. what is the probability that someone consumed less than 3030 gallons of bottled​ water?
d. 9999​% of people consumed less than how many gallons of bottled​ water?
a. the probability that someone consumed more than 3535 gallons of bottled water is

Answer 1

Per capita consumption of bottled water is approximately normally distributed with a mean of 34.7 and a standard deviation of 13 gallons.  You will need the Z-score table to convert it into percentiles

a. what is the probability that someone consumed more than 35 gallons of bottled water?
Z score of 35 gallons would be:
Z= (score-mean) / standard deviation
Z= (35-34.7) /13
Z= 0.02
The percentile of Z=0.02 is 0.5080 which means 50.8% people consume lower than 35 gallons per year. Then, the number of people consume higher than 35 gallons would be: 100%- 50.8%= 49.2%


b. what is the probability that someone consumed between 30 and 40 gallons of bottled water?
To count this, you need to find the number of people in 40 gallons percentile and subtract it with 30 gallons percentile
Z= (score-mean) / standard deviation
Z= (40-34.7) /13
Z= 0.41 ==> 65.91 percentile

Z= (score-mean) / standard deviation
Z= (30-34.7) /13
Z= -0.36 ==> 35.94 percentile

The probability that someone is consuming 30-40 gallon would be: 65.91%-35.94%= 29.97%


c. what is the probability that someone consumed less than 30 gallons of bottled water?
This question can be answered using the equation of the previous question
Z= (score-mean) / standard deviation
Z= (30-34.7) /13
Z=-0.36 = 35.94 percentile
The probability of someone consume less than 30 gallons would be: 35.94%


d. 99 % of people consumed less than how many gallons of bottled water?
This question asking for 99% percentile value. To solve it, you need to reverse the step from the previous question. The Z score of 99 percentile is 3.09. Then, the number of gallons for 99 percentile would be:
score= mean + (Z * standard deviation)
score= 34.7 + (3.09*13)
score= 34.7 + 40.17
score= 74.87