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# problem set leture3-4.pdf

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BUEC 232
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BUEC 232 Summer 2013 Data and Decisions I Lorene Linklater Problem Set – Lectures 3 & 4 1. A woman wrote to Dear Abby and claimed that she gave birth 308 days after her last visit from her husband, who was in the Navy. Lengths of pregnancy have a mean of 268 days and a standard deviation of 15 days. Is such a length unusual? What do you conclude? 2. British Columbians drink, on average, 78 litres of beer per year with a standard deviation of 25 litres. (a) Based on what you know about beer consumption, do you think this distribution is bell- shaped? Why? (b) At least what percentage of British Columbians would drink between (i) 20 and 136 litres of beer per year?(ii) 28 and 128 litres of beer per year? 3. You have \$3,000 to invest in the stock market. You are considering investing in one of two stocks. The last seven (and eight) weekly closing prices are provided below: New Age Technology: \$ 12 8.5 19 14 16 10 13.5 Ma Bell: \$75.5 82 72 69 83.5 77.5 78.5 72 (a) For each stock calculate the mean, median, mode, range and sample standard deviation. (b) Calculate the coefficient of variation for each stock. (c) Choose the most appropriate of the 6 measures to determine which stock is riskier. Why? 4. Having kept records for several months, Mrs. Lewis knows that it takes her on average 47.7 minutes with a standard deviation of 2.46 minutes to drive to work from her home in the suburbs. If she always starts out exactly one hour before she has to arrive at work, at most what percentage of the time will she arrive late? 5. The average height of adult males is 69 inches with a standard deviation of 3 inches. Assume that the height of men is bell-shaped. (a) How many standard deviations above the average height is a man who is (i) 72 inches tall? (ii) 78 inches tall? (b) At least how many standard deviations above the average height is a man who is in the top 2.5% of the adult male population? At least how many inches taller must he be? (c) For males, what is the minimum height needed to be in the top 2.5% in height? (d) What height does a male need to be to qualify as an outlier? 6. IQ scores were discussed in an article in the Atlantic Monthly. Adult IQ scores have a bell- shaped distribution with a mean of 100 and a standard deviation of 15. (a)What percentage of the population would have IQ scores between (i) 85 and 115? (ii) 70 and 130? (iii) 55 and 130? (b) What percentage of the population would have an IQ score of 115 or higher? (c) Genius is defined to be an IQ score of 145 or higher. What percentage of the population would be categorized as genius? (d) If there are 140,000 adults living in Burnaby how many geniuses should there be? (e) 95% of all adults should have IQ scores between what two values? Page 1 of 3 BUEC 232 Summer 2013 Data and Decisions I Lorene Linklater 7. The life of SuperDuper Tires has a bell-shaped distribution with a mean of 80,000 km and a standard deviation of 15,000 km. (a) The life of 68% of tires should be between what two values? (b) The life of 99.7% of tires should be between what two values? (c) What percentage of the population of tires should last between 50,000 and 110,000 km? (d) What percentage of the population of tires should last between 65,000 and 110,000 km? (e) What percentage of the population of tires should fail before 50,000 km? (f) What percentage of the population of tires should last between 50,000 and 125,000 km? (g) Is it likely that the tires will last longer than 125,000 km according to the empirical rule? Explain. (h) Among 4,000 tires, how many w
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