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. 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 they find that amount or less only 15% of the time, we need to find the 15th percentile of the normal distribution with a mean of 12 ounces and a standard deviation of 3 ounces. Using the z-score table, a z-score of approximately -1.04 corresponds to the 15th percentile. The formula for converting a z-score to a value in the distribution is: Value = Mean + (Z-score * Standard Deviation). Therefore, Value = 12 + (-1.04 * 3) = 8.88 ounces.

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