Gold miners in Alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1,000 tons of dirt is normally distributed. If the miners excavated 1,000 tons of dirt, how little gold must they have found such that they find that amount or less only 15% of the time?
A) −1.04
B) 1.04
C) 8.89
D) 15.12

Question

Quizplus · Accepted Answer

To find the amount of gold that is found 15% of the time or less, we look for the z-score corresponding to the 15th percentile in a standard normal distribution, which is approximately -1.04. Using the formula for converting a z-score to a raw score: X = μ + zσ, where μ is the mean (12 ounces), σ is the standard deviation (3 ounces), and z is the z-score (-1.04), we calculate X = 12 + (-1.04)(3) = 12 - 3.12 = 8.88, which rounds to 8.89 ounces.

Gold Miners in Alaska Have Found, on Average, 12 Ounces