Question

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?

Answer 1

0.4952 is the required probability.

Explanation:

We are given the following information in the question:

Mean, μ = 12

Standard Deviation, σ = 3

We are given that the distribution of amount of gold found per 1,000 tons of dirt is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(miners find between 10 and 14 ounces of gold)

`P(10 \leq x \leq 14) = P(\displaystyle(10 - 12)/(3) \leq z \leq \displaystyle(14-12)/(3)) = P(-0.667 \leq z \leq 0.667)\\\\= P(z \leq 0.667) - P(z < -0.667)\\= 0.7476- 0.2524 = 0.4952 = 49.52\%`

0.4952 is the probability that the miners find between 10 and 14 ounces of gold in the next 1,000 tons of dirt excavated.