Question

An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 256 watts with a standard deviation of 10 watts. What is the probability that the mean amplifier output would be greater than 254.7 watts in a sample of 53 amplifiers if the claim is true?

a. Use the Z-score formula to calculate the probability.

Answer 1

To find the probability of the sample mean being greater than 254.7 watts, the Z-score is calculated using the population mean, standard deviation, and sample size. The standard normal distribution table or calculator is then used to determine the probability.

Step-by-step explanation:

The operation manager needs to calculate the probability of obtaining a sample mean greater than 254.7 watts, given that the population mean is 256 watts and the standard deviation is 10 watts for a sample size of 53 amplifiers. To calculate this probability using the Z-score, we first need to find the standard error of the mean using the formula standard error = standard deviation / √n, where n is the sample size. We get a standard error of 10/√53. We then calculate the Z-score using the formula Z = (sample mean - population mean) / standard error. Lastly, we use the standard normal distribution table or a calculator to find the probability corresponding to the calculated Z-score.