Question

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 49 525 470 500 515 480 505 500 505 513 460 470
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
3. If he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control?
A) sample 1
B) sample2
C) sample 3
D) both samples 2 and 3
E) all samples are in control

Answer 1

Answer:

1) 515 hours

2) 495 hours

3) Sample 3

Explanation:

As given,

Sample                                                       Service life

1                                     495               500              505            500

2                                    525                515              505            515

3                                     470                480             460            470

a.)

Sample mean service for sample 2 = $\frac{525+515+505+515}{4} = \frac{2060}{4}$ = 515

Correct option is C.

b.)

Mean of the sampling distribution = Average of all the samples

Average of sample 1 = $\frac{495+500+505+500}{4} = \frac{2000}{4}$ = 500

Average of sample 2 =  $\frac{525+515+505+515}{4} = \frac{2060}{4}$ = 515

Average of sample 3 =  $\frac{470+480+460+470}{4} = \frac{1880}{4}$= 470

Now,

Mean of the sampling distribution = $\frac{500+515+470}{3} = \frac{1485}{3}$ = 495

Correct option is C.

c.)

For the sample to be in control, the Average has to be lie in between the upper and lower control limit

As

470 does not lie between 480 and 520

∴ we get

Sample 3 will be out of control.

Correct option is C.