Question

You want to know the percentage of utility companies that earned revenue greater than 95 million dollars. If the mean revenue was 70 million dollars and the data has a standard deviation of 13 million, find the percentage. Assume that the distribution is normal. Round your answer to the nearest hundredth.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the percentage of utility companies that earned revenue greater than 95 million dollars, we need to find the Z-score corresponding to 95 million dollars, then find the percentage of companies with revenue greater than that Z-score.

First, we calculate the Z-score:
Z = (X - μ) / σ
Z = (95 - 70) / 13
Z = 25 / 13
Z ≈ 1.92

Next, we look up the Z-score of 1.92 in a standard normal distribution table or use a calculator to find that approximately 97.84% of the data falls below a Z-score of 1.92.

Since we want to find the percentage of companies with revenue greater than 95 million dollars, we subtract 97.84% from 100%:
100% - 97.84% = 2.16%

Therefore, approximately 2.16% of utility companies earned revenue greater than 95 million dollars.