PROPER USAGE OF NORMDIST AND NORMINV FUNCTIONS , AS WELL AS SKETCHES OF NORMAL DISTRIBUTION ILLUSTRATIONS, FOR THE PROBLEMS

BMW Storms Ahead In 1959, BMW (Bayerische Motoren Werke) almost went bankrupt. BMW, German luxury-car makers, nearly sold out that year to Daimler-Benz, the maker of Mer- cedes-Benz cars. BMW held on and has spent the past three decades competing firercely with Mercedes for leadership in the luxury-car market. Finally, in 1992, BMW edged past Mercedes in worldwide sales. While Meroedes was forced to extend a holiday factory shutdown because of slow sales, BMW worked 30 shifts of overtime in 1992 to keep up with demand. In 1993, BMW sold around 590,000 cars worldwide, whereas Mercedes sold an estimated 530,000. BMW also beat Mercedes in the U.S. market by around 65,000 to about 63,000 cars. Just a few years ago, BMW sales were declining. In fact, the 1991 BMW sales fig- ures in the United States were down from a peak sales of almost 97,000 in 1986. when "yupple cars" were more in fashion. However, sales from 1991 to 1992 climbed 23.5% and have continued to increase The latest BMW models are larger and more luxurious than previous models, but their styling makes them look smaller than Mercedes when parked next to them This might seem like a disadvantage. However, consumers in the early 1990s were looking for cars that were not as big and expensive-looking, with an eye toward consumer quality and environmentalism. In addition, BMW has pulled ahead of Mercedes in management efficiency. Mercedes' new plant in Germany produces 360 cars per day using 5,500 employees. BMWs new plant in South Carolina uses only 2,000 employees to produce 400 cars per day. Another factor in BMW's success stems from its 3-Series cars which, though not glamorous, are elegant and environmentally friendly. After introducing the 3-Series sedan, BMW followed with a coupe, a convertible, a hatchback, and the U.S.-made 23 sports car. BMW does not have the same profit margins on the 3-Series as it does on its other cars, but the increased volume due to lower prices has kept showrooms busy and attracted younger buyers. Currently, BMW is producing around 600,000 cars per year. BMW retains an im- age of a select manufacturer that produces stylish, desirable automobiles. It has tar- geted its sales pitch to the younger yuppie market, whereas Mercedes-Benz has re- tained a more mature customer base. At the upper end, BMWs most expensive car has an average price of $83,400 and Mercedes' most expensive car sells for $132,000, on average DISCUSSION Suppose BMW company officials want to conduct a sales study for their United States market. Daily sales figures are kept over a period of several months, with a re- sulting mean of 247 cars sold per day and a standard deviation of 23 cars. An analy- sis of previous sales figures indicates that because of such factors as state of the econ- omy, season of the year, lending rates, and advertising efforts, sales figures vary from day to day but are approximately normally distributed. What proportion of the time are more than 200 cars sold in the U.S. market on a given day? What proportion of the time are more than 300 sold on a given day in the U.S. market? What proportion of the time does BMW sell between 225 and 275 cars in the U.S. market per day? To help in planning and staffing, BMW would like to know the least number of cars that it is likely to sell in one day. What number of cars sold per day is so low that a num- ber that low or lower would occur only about 1% of the time? What could market ing, production, and/or other functional areas of BMW learn from such information? BMW Storms Ahead In 1959, BMW (Bayerische Motoren Werke) almost went bankrupt. BMW, German luxury-car makers, nearly sold out that year to Daimler-Benz, the maker of Mer- cedes-Benz cars. BMW held on and has spent the past three decades competing firercely with Mercedes for leadership in the luxury-car market. Finally, in 1992, BMW edged past Mercedes in worldwide sales. While Meroedes was forced to extend a holiday factory shutdown because of slow sales, BMW worked 30 shifts of overtime in 1992 to keep up with demand. In 1993, BMW sold around 590,000 cars worldwide, whereas Mercedes sold an estimated 530,000. BMW also beat Mercedes in the U.S. market by around 65,000 to about 63,000 cars. Just a few years ago, BMW sales were declining. In fact, the 1991 BMW sales fig- ures in the United States were down from a peak sales of almost 97,000 in 1986. when "yupple cars" were more in fashion. However, sales from 1991 to 1992 climbed 23.5% and have continued to increase The latest BMW models are larger and more luxurious than previous models, but their styling makes them look smaller than Mercedes when parked next to them This might seem like a disadvantage. However, consumers in the early 1990s were looking for cars that were not as big and expensive-looking, with an eye toward consumer quality and environmentalism. In addition, BMW has pulled ahead of Mercedes in management efficiency. Mercedes' new plant in Germany produces 360 cars per day using 5,500 employees. BMWs new plant in South Carolina uses only 2,000 employees to produce 400 cars per day. Another factor in BMW's success stems from its 3-Series cars which, though not glamorous, are elegant and environmentally friendly. After introducing the 3-Series sedan, BMW followed with a coupe, a convertible, a hatchback, and the U.S.-made 23 sports car. BMW does not have the same profit margins on the 3-Series as it does on its other cars, but the increased volume due to lower prices has kept showrooms busy and attracted younger buyers. Currently, BMW is producing around 600,000 cars per year. BMW retains an im- age of a select manufacturer that produces stylish, desirable automobiles. It has tar- geted its sales pitch to the younger yuppie market, whereas Mercedes-Benz has re- tained a more mature customer base. At the upper end, BMWs most expensive car has an average price of $83,400 and Mercedes' most expensive car sells for $132,000, on average DISCUSSION Suppose BMW company officials want to conduct a sales study for their United States market. Daily sales figures are kept over a period of several months, with a re- sulting mean of 247 cars sold per day and a standard deviation of 23 cars. An analy- sis of previous sales figures indicates that because of such factors as state of the econ- omy, season of the year, lending rates, and advertising efforts, sales figures vary from day to day but are approximately normally distributed. What proportion of the time are more than 200 cars sold in the U.S. market on a given day? What proportion of the time are more than 300 sold on a given day in the U.S. market? What proportion of the time does BMW sell between 225 and 275 cars in the U.S. market per day? To help in planning and staffing, BMW would like to know the least number of cars that it is likely to sell in one day. What number of cars sold per day is so low that a num- ber that low or lower would occur only about 1% of the time? What could market ing, production, and/or other functional areas of BMW learn from such information