Question

An oil producer plans to sell 1 million barrels of crude oil one year from now. The oil price in one year is normally distributed with the mean of $80 per barrel and the standard deviation of $12 per barrel. What is the probability that the sales revenue is lower than $50 millions

A)0.62%

B)41.75%

C)58.25%

D)99.38%

Answer 1

Population mean = Mean price per barrel * No of barrels

Population mean = $80 * 1,000,000

Population mean = $80,000,000

Standard Deviation = Standard Deviation per barrel * No of barrels

Standard Deviation = $12 * 1,000,000

Standard Deviation = $12,000,000

Let us compute the z-score through the test statistic

Test Statistic = (Sample mean - Population mean) / Standard Deviation

Test Statistic = ($50,000,000 - $80,000,000) / $12,000,000

Test Statistic = -2.5

Z-score = -2.5

Using the Standard Normal cumulative distribution table N(- < Z < 2.5) = 0.9938

Probability of Sales revenue less than $50 million = N(- < Z < - 2.5)

Probability of Sales revenue less than $50 million = 1 - N(- < Z < 2.5)

Probability of Sales revenue less than $50 million = 1 - 0.9938

Probability of Sales revenue less than $50 million = 0.0062 or 0.62%