Problem 3-9

 1. d      2. a (c if 2 standard deviations are used to establish the limits.

 3. a     4. b     5. a     6. c     7. c     8. a     9. a     10. b

Problem 3-10

 1. The grand mean is 11.69. The mean of the ranges is .54.

    The values for the equation below are from Exhibit 3-9 and based on 6 items per sample.

   The upper limit is 11.69 + (.483)(.54) = 11.95

  The lower limit is  11.69 - (.483)(.54) = 11.429

 2. The limits for the range are based on the following equations.

 
  The upper limit is (2.004)(.54) = 1.08216

  The lower limit is (0)(.54) = 0

 3. Yes the process appears to be in control since all ten means are within the limits, although some of the individual observations are outside the limits.

Problem 3-11

 The original grand mean is 129.6/12 = 10.8

 The new grand mean is 120/12 = 10

 Note that every point in the new set of data is below the original mean. Unless the truck is being used for a different purpose (e.g., city driving vs. highway, heavy loads vs. light loads), it appears that it might be time for a tune up. Another possibility is that a different type of gas is being used. A different driver who drives less economically could also cause different results.