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 more than 16 ounces of gold in the next 1,000 tons of dirt excavated?
A) 0.0912
B) 0.4082
C) 0.5918
D) 0.9082

Question

Quizplus · Accepted Answer

First, we need to standardize the value of 16 ounces to find the corresponding z-score:

z = (16 - 12) / 3 = 1.33

Next, we use a standard normal distribution table or calculator to find the probability of getting a z-score greater than 1.33:

P(z > 1.33) = 0.0912

Therefore, the probability the miners find more than 16 ounces of gold in the next 1,000 tons of dirt excavated is 0.0912 or approximately 9.12%, which corresponds to choice (A).

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