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#### Panhandle Recycling is a company in Dothan, Alabama that recycles automobile catalytic converters

###### Statistics

Panhandle Recycling is a company in Dothan, Alabama that recycles automobile catalytic converters.Catalytic converters are part of a vehicle’s exhaust system. Emissions go through a ceramic filter thatcontains valuable metals, including platinum, palladium, and rhodium. Recyclers extract these metals from catalytic converters of junked cars, and resell them at the metals’current market prices.

Unfortunately for recyclers like Panhandle, there is no way to know exactly how much of each precious metal is inside any particular catalytic converter without actually cutting it apart. (The amount of the metals used to construct catalytic converters has varied across car makers and over time, though thereare typical “recipes”of combinations of metals.) On the other hand, Panhandle has extensive data on the contents of previously recycled catalytic converters. Based on this data, and the current market price of platinum, palladium, and rhodium, they estimate that the worth of any catalytic converter has the following probability distribution.

Worth of Converter \$1200 \$1800 \$2400 Probability 0.35 0.50 0.15

A local junkyard offers a load of 500 catalytic converters to Panhandle at a particular price. Panhandle needs to assess the worth of the entire load to decide whether to purchase it. Assume that the worth of any one converter is independent of the worth of the others.

1. (a) What is theexpected valueof the total worth of the 500 catalytic converters?

2. (b) What is thestandard deviationof the total worth?

3. (c) To cover its costs of processing and to insure itself a healthy profit in the face of uncertainty,

Panhandle typically would not pay a price higher than the 25thpercentile of the probability distribution associated with the worth of the load. (In other words, they would agree to a price only if there is a 75% chance that the load is worth more than that price.) Following this rule, what is the maximum price that Panhandle would be willing to pay to the junkyard for the load of 500 catalytic converters?