Question: The amount of toothpaste in a tube is normally distributed with a mean of 6.5 ounces and an s.d. of 0.8 ounces. The cost of

The amount of toothpaste in a tube is normally distributed with a mean of 6.5 ounces and an s.d. of 0.8 ounces. The cost of producing each tube is 50 cents. If in a quality control examination a tube is found to weigh less than 6 ounces, it is to be refilled to the mean value at a cost of 20 cents per tube. On the other hand, if the tube weighs more than 7 ounces, the company loses a profit of 5 cents per tube.
If 1000 tubes are examined,
a. How many tubes will be found to contain less than 6 ounces?
b. In that case, what will be the total cost of the refill?
c. How many tubes will be found to contain more than 7 ounces? In that case, what will be the amount of profits lost?

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