# Project #5310 - Statistics for Business

38.  Seventy percent of service calls regarding kitchen appliances involve a minor repair.  For example, the customer did not read the instructions correctly or perhaps failed to connect the appliance correctly.  These service calls cost \$75.  Service calls for major repairs are more expensive.  More than one-half of service calls for major repairs cost the customer \$200 or more.  What’s the probability that a randomly selected service call cost \$200 or more?

40.  Some of the managers at a company have an MBA degree. Of the managers at the level of director or higher, 60% have an MBA. Among other managers of lower rank, 35% have an MBA.  For this company, 15% of managers have a position at the level of director or higher.  If you meet an MBA from this firm, what are the chances that this person is a director (or higher)?

42.  Many retail stores open their doors early the day after Thanksgiving to attract shoppers to special bargains.  A shopper wanting two medium blouses heads for the sale rack, which is a mess, with sizes jumbled together.  Hanging on the rack are 4 medium, 10 large, and 6 extra-large blouses.  Find the probability of each event described.

(a)     The first two blouses the grabs are wrong size.

(b)   The first medium blouse she finds is the third one she checks.

(c)    The first four blouses she picked are all extra-large.

(d)   At least one of the first four blouses she checks is a medium.

44.  Among employees at a retailer, there is a 15% chance that an employee will be absent  from work for some reason.  The floor manager has been talking with two randomly selected employees each day to get suggestions to improve sales.

(a)  What is the probability that the first employee he chooses to speak is absent?

(b)  Describe the probability that the second employee he chooses to speak wit is absent, assuming that the first employee is present.  Is it higher, lower, or the same as the probability in part (a)?

(c)  Should your answers to part (a) and (b) match?  Explain why or why not.

46.  Modern assembly relies on parts built to specifications (specs) so that the components fit together to make the whole.  An appliance requires two components, Type A and Type B. supplied by different manufacturers.  A robot randomly selects a component from a batch of Type A components and a second component from batch of Type B components.  The appliance works only if both components are within specifications.  It is known that 5% of type A components and Type B components are out of specifications.

(a)  What is the probability that the appliance produce by the robot selecting one component from each batch at random works?

(b)  The robot tests the appliance as it is assembled.  It discovers that the current applicance does not work because the parts are not compatible.  What is the probability that component that is out of spec is the Type A component?

48.  A company buys components that are of higher quality than the other.  The high-quality supplier, Supplier B. has a defect rate of 2%.  The low –quality supplier, Supplier B, has a defect rate of 10% but offers lower prices.  This company buys in equal amount from both suppliers, with half of the orders going to each supplier.

(a)  What is the probability that a component to be installed is defective?

(b)  If a defective component is found, what is the probability it came from Supplier A?

50.  A survey reports that 62% of callers to a help desk complain about the service if they think they spoke to a foreign agent, compared to 31% who complaints if they think they spoke to a native agent.  Suppose that 40% of all calls to service centers are handled by agents in the United States.  If a caller complains, what is the probability she was dealing with a foreign agent?

52.  Suppose that 20% of the clerical staff in an office smoke cigarettes.  Research shows that 60% of smokers and 15% of nonsmokers suffer a breathing illness by age 65.

(a)  Do these percentages indicate that smoking and this breathing illness are independent?

(b)  What’s the probability that a randomly selected 65-year-old employee who has this breathing illness smokes?

 Subject Business Due By (Pacific Time) 5/1/2013
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