Racell Corporation is a food manufacturer which produces several different kinds of cereals.

Krinkles, one of Racell’s cereals is packaged and sold in a 500-gram box. The filling equipment used to fill the boxes cannot be set precisely enough to guarantee that each box will contain exactly 500 grams. The volume by weight of cereal put in the boxes is normally distributed with a standard deviation of 12 grams. The filling equipment can be adjusted to vary the mean fill, but the standard deviation is constant. Management has specified that the filling equipment be set so that no more than three boxes out of 100 have less than 500 grams. If a box does contain less than 500 grams, the box is emptied and the contents are reentered into the filling process.

The manufacturer of the filling equipment being used by Racell has informed the company that an attachment is available which can improve the performance of the filling operation. The manufacturer estimates that the standard deviation of the filling operation for Krinkles can be reduced to 8 grams. The attachment would have to be replaced after 150,000 boxes were filled and would cost $1,500.

Racell sells 900,000 boxes of Krinkles annually. Krinkles are sold on the retail market for $1.35 a box; the wholesale price is $1.10 a box. The standard variable production cost is $.75 to produce 500 grams. : klop855

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2 Area Area 2 Area 1.0 .341 1.7 .455 2.4 .492 1.1 .364 1.8 .464 2.5 .494 1.2 .385 1.9 .471 2.6 .495 1.3 .403 2.0 477 2.7 .497 1.4 419 2.1 .4821 2.8 .497 1.5 .433 2.2 .486 2.9 498 1.6 .445 2.3 .489 3.0 .499 Required: a Calculate the mean fill setting required for Racell Corporation's filling equipment in order to meet the specifications set by management assuming the new attachment is not added. b Should Racell Corporation acquire the attachment which would reduce the standard deviation of the filling process from 12 to 8 grams? Support your decision with appropriate calculations. (CMA Adapted.)