North Dakota Mining (NDM) describes its estimate of the amount of oil it will produce next year from its western North Dakota operations with a normal distribution.The distribution is centered on 5.2 million barrels and has a standard deviation of .7 million barrels.According to this distribution, how likely is it that NDM's production will be less than 4.5 million barrels?
A).1736
B).1587
C).2019
D).2794
E).2823

Question

Quizplus · Accepted Answer

To find the probability that NDM's production will be less than 4.5 million barrels, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (4.5 million barrels), $\mu$ is the mean (5.2 million barrels), and $\sigma$ is the standard deviation (0.7 million barrels). Plugging in the values, we get $Z = \frac{4.5 - 5.2}{0.7} = -1$. Looking up the Z-score of -1 in a standard normal distribution table gives a probability of approximately 0.1587, or 15.87%.

North Dakota Mining (NDM) Describes Its Estimate of the Amount