Question

A production line producing motors completes a run of 40 units. All 40 motors are performance tested and the average shaft power output is 125.0 kW with a standard deviation of 3.0 kW. Determine the 90% confidence interval of the mean shaft power output of the run.

Answer 1

The 90% confidence interval for the mean shaft power output of the run is calculated to be from 124.22 kW to 125.78 kW, using the z-score for 90% confidence and the standard deviation with the given data.

Step-by-step explanation:

To determine the 90% confidence interval for the mean shaft power output of a production line that has an average output of 125.0 kW with a standard deviation of 3.0 kW for a sample size of 40 units, we will use the following formula:

Confidence Interval = µ ± (z * (σ / √n))

where µ is the sample mean, σ is the standard deviation, n is the sample size, and z is the z-score corresponding to the desired confidence level.

To find the appropriate z-score for a 90% confidence level, we refer to the standard normal distribution table. The z-score that corresponds to a 90% confidence level (with 5% in each tail) is approximately 1.645.

Confidence Interval = 125.0 ± (1.645 * (3.0 / √40))

Confidence Interval = 125.0 ± (1.645 * (3.0 / 6.3246))

Confidence Interval = 125.0 ± (1.645 * 0.4743)

Confidence Interval = 125.0 ± 0.7805

Therefore, the 90% confidence interval for the mean shaft power output is 124.22 kW to 125.78 kW.