1) Buyers often insist on discounts for large orders. Experience shows that the amount of their required discounts ranges from 0 to 18%, with a uniform distribution.
a) Write the mathematical expression for the probability density function of the percent discount.
b) What is the probability that a new buyer will expect a discount that is between 5% and 12%?
2) A study from Consumer Reports showed that the lifetime of TV sets is normally distributed with mean of 8.2 years and standard deviation of 1.3 years. If is desired to offer a replacement guarantee on the 2% of sets with the shortest lifetimes for how long should TV's be guaranteed?
3) Suppose that weights of bags of potato chips coming from a factory follow a normal distribution with mean 12.8 ounces and standard deviation .6 ounces. If the manufacturer wants to keep the mean at 12.8 ounces but adjust the standard deviation so that only 1% of the bags weigh less than 12 ounces, how small does he/she need to make that standard deviation?
4) Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council's GMAT examination. (From GMAT Examinee Score Interpretation Guide, Graduate Management Admissions Council, 2000. Found online at www.gmac.com.) Total scores on the GMAT for the more than 500,000 people who took the exam between April 1997 and March 2000 are normally distributed with mean 527 and standard deviation 112.
(a) What percent of test takers have scores above 500?
(b) What GMAT scores fall in the lowest 25% of the distribution?
(c) How high a GMAT score is needed to be in the highest 5%?
5) The National Collegiate Athletic Association (NCAA) requires Division I athletes to score at least 820 on the combined Mathematics and Verbal parts of the SAT to compete in their first college year. (Higher scores are required for students with poor high school grades.) In 2000, the scores of the 1,260,000 students taking the SATs were approximately Normal with mean 1019 and standard deviation 209. What percent of all students had scores less than 820?
6) Let X be the amount of time (in minutes) a postal clerk spends with his/her customer. The time is known to have an exponential distribution with the average amount of time equal to 4 minutes. Find the probability that a clerk spends four to five minutes with a randomly selected customer.