Question

Bob is a builder. He finds that the weekly operating cost varies from week to week. Assuming weekly earnings are normally distributed with a mean of $1,200 and a standard deviation of $400. What is the probability that the weekly earnings of Bob are between $800 and $1,000? Round your answer to 3 decimal places.

Answer 1

To find the probability that Bob's weekly earnings are between $800 and $1,000, we calculate the z-scores for both values and use the standard normal distribution table. The probability is found using the corresponding z-score for the range.

Step-by-step explanation:

To find the probability that Bob's weekly earnings are between $800 and $1,000, we need to calculate the z-scores for both values and use the standard normal distribution table. The z-score formula is z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

• For $800, the z-score is z = (800 - 1200) / 400 = -0.5
• For $1,000, the z-score is z = (1000 - 1200) / 400 = -0.5

Using the standard normal distribution table, we can find the probability corresponding to the z-score -0.5, which is 0.3085. Therefore, the probability that Bob's weekly earnings are between $800 and $1,000 is 0.3085.