Assignment #02 1. According to a Sallie Mae survey and credit bureau data, in 2008, college students carried an average of $3173 debt on their credit cards ( USA TODAY , April 13, 2009). Suppose that current credit card debts for all college students have a normal distribution with a mean of $3173 and a standard deviation of $800. Find the probability that credit card debt for a randomly selected college student is between $2109 and $3605. 2. A racing car is one of the many toys manufactured by Mack Corporation. The assembly times for this toy follow a normal distribution with a mean of 55 minutes and a standard deviation of 4 minutes. The company closes at 5 P.M. every day. If one worker starts to assemble a racing car at 4 P.M., what is the probability that she will finish this job before the company closes for the day?
3. Hupper Corporation produces many types of soft drinks, including Orange Cola. The filling machines are adjusted to pour 12 ounces of soda into each 12-ounce can of Orange Cola. However, the actual amount of soda poured into each can is not exactly 12 ounces; it varies from can to can. It has been observed that the net amount of soda in such a can has a normal distribution with a mean of 12 ounces and a standard deviation of .015 ounce. (a) What is the probability that a randomly selected can of Orange Cola contains 11.97 to 11.99 ounces of soda? (b) What percentage of the Orange Cola cans contain 12.02 to 12.07 ounces of soda?
4. According to the 2007 American Time Use Survey by the Bureau of Labor Statistics, employed adults living in households with no children younger than 18 years engaged in leisure activities for 4.4 hours a day on average ( Source: http://www.bls.gov/news.release/at http://www.bls.gov/news.release/atus.nr0.htm). us.nr0.htm). Assume that currently such times are (approximately) normally distributed with a mean of 4.4 hours per day and a standard deviation of 1.08 hours per day. Find the probability that the amount of time spent on leisure activities per day for a randomly chosen individual from the population of interest (employed adults living in households with no children younger than 18 years) is (a) between 3.0 and 5.0 hours per day (b) less than 2.0 hours per day
5. The Bank of Connecticut issues Visa and MasterCard credit cards. It is estimated that the balances on all Visa credit cards issued by the Bank of Connecticut have a mean of $845 and a standard deviation of $270. Assume that the balances on all these Visa cards follow a normal distribution. (a) What is the probability that a randomly selected Visa card issued by this bank has a balance between $1000 and $1440? ha s a balance of $730 or more? (b) What percentage of the Visa cards issued by this bank has
6. According to a 2004 survey by the telecommunications division of British Gas (Source : http://www.literacytrust.org.uk/Database/texting.html#quarter), Britons spend an average of 225 minutes per day communicating electronically (on a fixed landline phone, on a mobile phone, by emailing, by texting, and so on). Assume that currently such times for all Britons are normally distributed with a mean of 225 minutes per day and a standard deviation of 62 minutes per day. What percentage of Britons communicate electronically for (a) less than 60 minutes per day (b) more than 360 minutes per day (c) between 120 and 180 minutes per day (d) Between 240 and 300 minutes per day?
7. Almost all high school students who intend to go to college take the SAT test. In a recent test, the mean SAT score (in verbal and mathematics) of all students was 1020. Debbie is planning to take this test soon. Suppose the SAT scores of all students who take this test with Debbie will have a normal distribution with a mean of 1020 and a standard deviation of 153. What should her score be on this test so that only 10% of all examinees score higher than she does?
8. According to the records of an electric company serving the Boston area, the mean ele ctricity consumption during winter for all households is 1650 kilowatt-hours per month. Assume that the monthly electric consumptions during winter by all households in this area have a normal distribution with a mean of 1650 kilowatt-hours and a standard deviation of 320 kilowatt-hours. The company sent a notice to Bill Johnson informing him that about 90% of the households use less electricity per month than he does. What is Bill Johnson’s monthly electricity consumption?
9. Rockingham Corporation makes electric shavers. The life (period before which a shaver does not need a major repair) of Model J795 of an electric shaver manufactured by this corporation has a normal distribution with a mean of 70 months and a standard deviation of 8 months. The company is to determine the warranty period for this shaver. Any shaver that needs a major repair during this warranty period will be replaced free by the company. (a) What should the warranty period be if the company does not want to replace more than 1% of the shavers? (b) What should the warranty period be if the company does not want to replace more than 5% of the shavers?
