The chief chemist for a major oil and gasoline production company claims that the regular unleaded gasoline produced by the company contains on average 4 ounces of a certain ingredient.The chemist further states that the distribution of this ingredient per gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2 ounces.What is the probability of finding an average less than 3.85 ounces of this ingredient from 64 randomly inspected 1-gallon samples of regular unleaded gasoline?
A).1587
B).8413
C).1357
D).8643

Question

Quizplus · Accepted Answer

The probability of finding an average less than 3.85 ounces of this ingredient from 64 randomly inspected 1-gallon samples of regular unleaded gasoline is 0.1587. This is because the distribution of this ingredient per gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2 ounces, and the average of 64 randomly inspected 1-gallon samples will be normally distributed with a mean of 4 ounces and a standard deviation of 1.2 ounces / sqrt(64) = 0.15 ounces. Therefore, the probability of finding an average less than 3.85 ounces is the area under the normal distribution curve to the left of 3.85 ounces, which is 0.1587.

The Chief Chemist for a Major Oil and Gasoline Production