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 this service life 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

1. What is the sample mean service life for sample 2?

a. 460 hours
b. 495 hours
c. 515 hours
d. 525 hours

2. What is the mean of the sampling distribution of sample means for whenever service life is in control?

a. 250 hours
b. 470 hours
c. 495 hours
d. 500 hours
e. 515 hours

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joaobezerra joaobezerra · Answer 1 · 2021-03-19T19:44:41+01:00

Answer:

1. c. 515 hours

2. c. 495 hours

Step-by-step explanation:

Sample mean:

Sum of all values in the sample divided by the number of values.

1. What is the sample mean service life for sample 2?

Sample 2 has four values, which are:

525 515 505 515

So

[tex]M = \frac{525+515+505+515}{4} = 515[/tex]

The answer is given by option C.

2. What is the mean of the sampling distribution of sample means for whenever service life is in control?

3 samples, 12 total values. We find the mean of all these values. So

[tex]M = \frac{495+500+505+500+525+515+505+515+470+480+460+470}{12} = 495[/tex]

The answer is given by option C.