The force needed to remove the cap from a medicine bottle is an important feature of the product because requiring too much force may cause diffi culty for elderly patients or patients with arthritis or similar conditions. Table 6E.17 presents the results of testing a sample of 68 caps attached to bottles for the force (in pounds) required for removing the cap. 

(a) Construct a stem-and-leaf diagram of the force data.

(b) What are the average and the standard deviation of the force?

(c) Construct a normal probability plot of the data and comment on the plot.

(d) If the upper specification on required force is 30 pounds, what proportion of the caps do not meet this requirement?

(e) What proportion of the caps exceeds the average force plus 2 standard deviations?

TABLE ˆ™ 6E.17 Force to Remove Bottle Caps

(f) Suppose that the fi rst 36 observations in the table come from one machine and the remaining come from a second machine (read across the rows and the down). Does there seem to be a possible difference in the two machines? Construct an appropriate

graphical display of the data as part of your answer.

(g) Plot the first 36 observations in the table on a normal probability plot and the remaining observations on another normal probability plot. Compare the results with the single normal probability plot that you constructed for all of the data in part (c).

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