The amount of natural gas that Taylor Exploration extracts daily at its Cane Creek site in Utah has a normal distribution, with an average of 82,300 cubic feet and a standard deviation of 12,400 cubic feet.On a randomly selected day, how likely is it that more than 67,000 cubic feet are extracted?
A).6734
B).7546
C).6219
D).7830
E).8907

Question

Quizplus · Accepted Answer

To find the probability of extracting more than 67,000 cubic feet of natural gas, we first calculate the z-score for 67,000 cubic feet using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value of interest (67,000 cubic feet), $\mu$ is the mean (82,300 cubic feet), and $\sigma$ is the standard deviation (12,400 cubic feet). The z-score is $z = \frac{(67,000 - 82,300)}{12,400} = -1.233$. Looking up this z-score in a standard normal distribution table or using a calculator, we find that the area to the right of this z-score (which represents the probability of extracting more than 67,000 cubic feet) is approximately 0.8907 or 89.07%. This means there is an 89.07% chance of extracting more than 67,000 cubic feet of natural gas on a randomly selected day.

The Amount of Natural Gas That Taylor Exploration Extracts Daily