A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results: Sample Service Life hours) 1 495 500 505 500 2 525 515 505 515 3 470 480 460 470 What is the sample means service life for sample 2

The sample mean service life for sample 2 is 515 hours.

Step-by-step explanation:

The design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces.

The distribution of service life in control is, normal with parameters,

Mean (μ) = 500 hours

Standard deviation (σ) = 20 hours

The random sample of 4 headlamps from 3 different production batches is:

Sample 1: 495, 500, 505, 500

Sample 2: 525, 515, 505, 515

Sample 3: 470, 480, 460, 470

The sample mean is a statistic, defined as the average value of the data in the sample.

It is computed using the formula:

Compute the sample mean service life for sample 2 as follows:

Thus, the sample mean service life for sample 2 is 515 hours.