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QMS 102 Module 10 Questions Fall 2014




Module 10 Questions;1. The lifetime of a certain brand of tire is normally distributed with a mean of 80,000;km. and standard deviation of 7,000 km. The tire carries a warranty for 68,000 km.;a) What is the probability that the tire you recently purchased will last at most 81,000;km.?;b) What percent of this brand of tire will fail before the warranty;expires? % format{~.dd};c) What should the mileage warranty be so that only 1% of the tires need to be;replaced under warranty? km. format{ w};2. A firm's marketing manager believes that total sales for next year can be;represented by a normal distribution, with a mean of $2.4 million and a standard;deviation of $350,000. The firm has fixed costs of $1.6 million.;a) What is the probability that the firm's sales will be less than $3.4 million?;b) What is the probability that the firm will have sufficient sales to cover fixed;costs?;c) What is the probability that the firm's sales will be within $140,000 of the expected;sales?;d) Determine the sales level that has only a 7% chance of being;exceeded. $ million. format{~.dd};3. The owner of a convenience store has copies of the local newspaper delivered early;each morning. The demand for papers is normally distributed with a mean of 76 and a;standard deviation of 17.;{Assume daily demand is continuous};a) What is the probability that there will not be enough newspapers to meet demand if;the owner orders 68 copies?;b) How many copies should be ordered so that the probability of "selling out" is at;most 13%? papers.;4. An investment broker reports that the annual returns on common stock and;municipal bonds are both normally distributed. The stocks have a mean return of;11.4% with a standard deviation of 19.8%. On the other hand the bonds have a mean;return of 6.2% with a standard deviation of 10.6%.;a) If you are a conservative investor and just don't like to lose money, which type of;investment should you choose?;If you made this selection, what would be your probability of losing money?;b) If you are more ambitious an investor and would like to have the best chance of;making more than 3%, which investment should you choose?;If you made this choice, what would be the probability of making more than 3%?;5. In the movie Forest Gump, the public school required an IQ of at least 70 to be;admitted.;a) If IQ test scores are normally distributed with a mean of 100 and a standard;deviation of 17, what percent of children would qualify for admittance to the;school? % format{~.dd};b) If the public school wished to have 85% of all children qualify for admittance, what;minimum IQ test score should be required for admittance? format{ ~.d};6. At a certain university the cumulative grade point average (CGPA) of first year;students usually averages 2.81 with a standard deviation 0.56. It has been found that;the marks are usually approximately normally distributed.;a) What is the probability that a student will have a CGPA that is between 1 and 3?;b) What percent of students will be on probation, i.e. their CGPA is less than;2? % format{~.dd};c) Academic scholarships are awarded to the top 2% of first year students. What;minimum CGPA is needed to receive a scholarship? format{ ~.d}


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