Math Quiz

Math Quiz: A small business just leased a new computer and color laser printer for 3 years. The service contract for the computer offers unlimited repairs for a fee of $100 a year plus a $25 service charge for each repair needed. The company’s research indicates that during a given year 86% of these computers need no repairs, 9% need to be repaired at least once, 4% twice, and 1% 3 times, and none required more than three repairs. What is the standard deviation in the number of repairs for this kind of computer per year? Round to two decimal places.

  1. For quality control purposes, a company that manufactures copper sheets routinely takes samples from its production process. Since its product is often used for decorative purposes, one inspection check involves counting the number of imperfections or flaws on sheets that measure 36 Sq ft. Suppose the average number of imperfections per sheet of this size is 3 and the number of imperfections per sheet follows a Poisson model.   What’s the probability that a sheet of this size has no more than 2 imperfections?  Round to four decimal.
  2. It has been reported that men are more likely than women to participate in online auctions. In this same survey, 45% of respondents were men and 38% were men that had participated in online auctions. What is the probability that a respondent selected at random is female and has never participated in an online auction?  Round to two decimal places.
  3. A manufacturer claims that its drug test will detect steroid use (that is showing positive for an athlete who uses steroids) 95% of the time. Further, 15% of all steroid-free individuals also test positive. 10% of the rugby team members use steroids. Your friend on the rugby team has just tested positive. What does the correct probability tree look like?

Key:       S  uses steroids                 $  does not use steroids

+  test positive                                  _  test negative

  1. Here is the five-number summary for salaries of U.S. marketing managers.:
Min Q1 Median Q3 Max
46360 69693 77020 91750 129420

What’s the IQR?

  1. Internet service providers (ISP) need to resolve customer problems as quickly as possible. For one ISP, past data indicates that the likelihood is .80 that the customer calls regarding internet service interruptions are resolved within an hour. For the next 10 customer calls about interrupted service, what is the probability that exactly 7 will be resolved within one hour? Round to four decimal places.
  2. Suppose a sample of 60 cans of soda has a mean of 112.1 ounces and a standard deviation of 0.05 ounces. If a can of soda has 12 ounces, what is its corresponding Z-score? Round to one decimal place. Get homework help here
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