To calculate: The expected cost for car owners who come in for repair of this problem.
$133.85.
Given information:
At the brake shop, the simplest fix is to clean and lubricate the caliper. This costs $50 and will work in 35% of cases. In 90% of the cars with a more serious problem, the caliper must be replaced at a cost of $85 for the pan and $75 for the labor to install it. The remaining cars need a complete brake overhaul that costs$350.
Formula used:
The expected value (or mean) is the sum of the product of each possibility x with its probability P(x):
Calculation:.
Given:
The simplest fix cost $50 and occurs in about 35% of the cases.
P($50) = 35% = 0.35
The remaining 100%-35% = 65% of the cases are serious, while 905 of the case have a total cost of $85+$75 = $160
Thus, 65%×90% = 0.65×0.90 = 0.585 of the cases.
P($160) = 65%×90% = 0.65×0.90 = 0.585 = 58.5%
There are then 100%-35%-58.5% = 6.5%case remaining, which have a total cost of $350.
P($350) = 6.5% = 0.065.
The expected value (or mean) is the sum of the product of each possibility x with its probability P(x):
Thus, the expected cost is $133.85.
Chapter 10 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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