Question

A machine used for filling aluminum cans with soda has a known standard deviation of 0.2 oz. the target mean is 12 oz . the project manager will shut the plant down if the cans are more than. 3 oz from the mean in either way. what is the probability of manager shutting down the plant?

Answer 1

The probability of the manager shutting down the plant is 93.32%.

Step-by-step explanation:

To find the probability of the manager shutting down the plant, we need to calculate the z-score for the given difference from the mean. The difference in weight allowed is 0.3 oz, and the standard deviation is 0.2 oz. The formula for calculating the z-score is: z = (x - μ) / σ, where x is the difference from the mean, μ is the mean, and σ is the standard deviation.

Substituting the values into the formula, we get z = (0.3 - 0) / 0.2 = 1.5.

To find the probability of the manager shutting down the plant, we need to find the area under the normal distribution curve to the left of the z-score of 1.5. Using a standard normal distribution table or a calculator, we find that the probability is approximately 0.9332, or 93.32%.

Therefore, the probability of the manager shutting down the plant is 93.32%.