Question

The mean output of a certain type of amplifier is 498 watts with a standard deviation of 12 watts.

If 86 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 1.1 watts? Round your answer to
four decimal places.

Answer 1

The probability that the mean of the sample would differ from the population mean by less than 1.1 watts is approximately 0.8023.

Step-by-step explanation:

To find the probability that the mean of the sample would differ from the population mean by less than 1.1 watts, we can use the standard deviation of the sample mean, also known as the standard error. The formula for the standard error is:

Standard Error = Standard Deviation / Square Root of Sample Size

Since the standard deviation of the population is given as 12 watts and the sample size is 86, we can calculate the standard error:

Standard Error = 12 / √86 ≈ 1.2943 watts

Next, we need to find the z-score corresponding to a difference of 1.1 watts:

Z-Score = Difference / Standard Error = 1.1 / 1.2943 ≈ 0.8503

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than 0.8503, which is approximately 0.8023.