Final Answer:
We can use the cumulative distribution function (CDF) of the data provided.Thus correct option is a. The probability that someone consumed more than 44 gallons of bottled water is 0.15 (rounded to four decimal places).
Step-by-step explanation:
To find the probability of someone consuming more than 44 gallons of bottled water, let's use the standard normal distribution formula:
Given:
Mean (μ) = 35 gallons
Standard deviation (σ) = 8 gallons
Value (X) = 44 gallons
First, we'll calculate the Z-score using the formula: Z= X−μ / σ
Z= 44−35 / 8 = 9/ 8 =1.125
Now, we need to find the probability associated with this Z-score using a standard normal distribution table or calculator. The probability of Z = 1.125 is the area under the standard normal curve to the right of this Z-score.
Using a Z-table or a calculator, the probability corresponding to Z = 1.125 is approximately 0.8708. However, since we're interested in the probability of consuming more than 44 gallons (which is to the right of 44 gallons on the distribution), we'll subtract this probability from 1 to find the area to the right of 44 gallons:P(Z>1.125)=1−0.8708=0.1292
Therefore, the probability that someone consumed more than 44 gallons of bottled water, based on the assumed mean of 35 gallons and a standard deviation of 8 gallons, is approximately 0.1292 or 12.92%.
This calculation involves determining the area under the normal curve beyond 44 gallons, indicating the likelihood of consumption exceeding this value within the specified distribution parameters.Thus correct option is a. The probability that someone consumed more than 44 gallons of bottled water is 0.15 (rounded to four decimal places).