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. What is the probability the miners find between 10 and 14 ounces of gold in the next 1,000 tons of dirt excavated?
A) 0.2514
B) 0.4950
C) 0.5028
D) 0.7486

Question

Quizplus · Accepted Answer

To find the probability of finding between 10 and 14 ounces of gold, we use the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For X = 10, Z = (10 - 12) / 3 = -2/3. For X = 14, Z = (14 - 12) / 3 = 2/3. Looking these Z-scores up in a standard normal distribution table or using a calculator, the probability of being between these Z-scores is approximately 0.4950.

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