Exhibit 6-2.Gold miners in Alaska have found,on average,12 ounces of gold per 1000 tons of dirt excavated with a standard deviation of 3 ounces.Assume the amount of gold found per 1000 tons of dirt is normally distributed. Refer to Exhibit 6-2.If the miners excavated 1000 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)8.88
D)15.12

Question

Quizplus · Accepted Answer

To find the amount of gold such that only 15% of the time they find that amount or less, we need to find the z-score that corresponds to the 15th percentile of a standard normal distribution, which is approximately -1.04. Using the formula: X = μ + Zσ, where μ = 12, σ = 3, and Z = -1.04, we calculate X = 12 + (-1.04)(3) = 8.88 ounces.