Sam Spade is owner and general manager of the Sam Spade Candy Company. One of the popular products manufactured by SSCC is the Gummy Falcon. (Below is a picture of Sam Spade admiring one of his Gummy Falcons.) This product was created over five years ago by Spade following the popularity of such confections as Gummy Bears, Gummy Worms, and so on. Gummy Falcons are made of black licorice molded in the shape of a falcon. Spade had initially encountered difficulty getting Gummy Falcons approved by the FDA, since the only ingredient listed on the package is "the stuff that dreams are made of."
The manufacturing process for Gummy Falcons has been designed so that the average weight of all Gummy Falcons is 2.50 ounces. The weights of the individual Gummy Falcons vary around the mean due to various random influences. The extent of this variation is inherent in the design of the manufacturing process and is controllable by the selection of the equipment which is used. As would be expected, the level of weight variation is inversely related to the cost of the production equipment. SSCC selected a production process for Gummy Falcons in which the weights of individual Gummy Falcons were normally distributed with a standard deviation of 0.15 ounces.
Assume that a Gummy Falcon is randomly selected from a large batch that has just been completed. What is the probability that the Gummy Falcon will weigh more than 2.60 ounces?
To maintain good customer relations, SSCC has a goal that no more than 5 percent of the Gummy Falcons weigh less than 2.25 ounces. Is this goal being met?
Suppose Sam Spade inspects 10 Gummy Falcons. What is the probability that the average weight of the ten Gummy Falcons is more than 2.60 ounces?