A local children's boutique specializes in formal wear for young girls. It has recently hired a new seamstress. To assure the dresses have standard sizes, twenty samples of each 12 dresses that were labeled 3T were sampled
The average length from shoulder to hemline measured 21 inches with a range of 0.5 inches. A sample has just been taken with the following lengths: 21.25, 22.0, 21.5, 20.75, 21.25, 21.35, 21.35, 21.35, 21.35, 21.35, 21.35, and 21.35. Is the new seamstress performing at an acceptable quality level?
UCL = 21 + 0.5(0.266 ) = 21.133
LCL = 21 - 0.5(0.266 ) = 20.867
Range UCL = 1.716 * 0.5 = 0.858
LCL = 0.284 * 0.5 = 0.142
The new seamstress is not performing at an acceptable level because both the range of this last sample (1.25 ) and the x-bar (21.35 ) are too high.
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