SAMPLE APPLICATIONS OF BINOMIAL AND NORMAL DISTRIBUTIONS Airline Overbooking An airline has found that there is a 10-percent chance that any given person with a plane reservation will fail to show up. Suppose 350 individuals have been booked for a flight which has only 320 seats. What is the probability that everyone who shows up will be seated? (Answer: 0.8365) Hospital Ward Staffing Each infant in a pediatric ward needs a nurse's attention 15-percent of the time. Suppose there are 120 infants in the ward and 20 nurses on call. What percentage of the time will some infant go unattended? (Answer: 26.11-percent) Direct Mail Solicitation A mail solicitation is sent to 10,000 individuals, each of whom has a 9-percent chance of responding. What is the probability that at least 850 individuals will respond? (Answer: 0.9599) Opinion Polling Seventy-five percent of the voters in a certain district favor a tax cut. Suppose 200 voters are sampled at random. What is the probability that between 70-percent and 80-percent of those sampled (inclusive) will favor a tax cut? (Answer: 0.9146) True-False Examination A true-false exam contains 100 questions, each worth one point. If a student guesses the answer to each question at random, what is the probability that he will score at most 60? (Answer: 0.9821) Highway Traffic Speeds The speeds of cars on a certain interstate highway are found to be normally distributed, with mean 61.3 mph and standard deviation 8.4 mph. What percentage of the cars are observing the speed limit of 55 mph? (Answer: 22.66-percent) _________________________________________________________________ From: Daniel Gallin, "Finite Mathematics," Scott-Foresman (1984). Computer Equipment Failure Originally Posted by Just Fred on 11-06-2009 at 01:43 PM I still remember when disk manufacturers used to talk about "mean time between failure" (MBTF) and how disks don't fail for *decades.* So I've had this less than the warranty period and I'm out nearly a terabyte of data... Posted by Hayne (Moderator) on 11-06-2009 at 3:06 PM You might merely be one of the unlucky ones. The "mean time between failures" is just a mean (average) of some probability distribution. If we assume that it's a "normal distribution" with a mean of 10 years and a standard deviation of 3 years, then out of a million drives: about 1000 (0.1%) will fail in less than one year about 20000 (2%) will fail in less than 4 years about 160000 (16%) will fail in less than 7 years Drug Efficacy The recovery rate for a certain disease is 60-percent. A pharmaceutical house claims that its new drug increases the chance of recovery to 80- percent. Suppose the drug is given to 50 patients with the disease, and 35 of them recover. Then: (a) What is the probability of a result this low, if the maker's claim is true? (Answer: 0.0297) (b) What is the probability of a result this high, if in fact the drug is worthless? (Answer: 0.0409) College Entrance Exams Scholastic Aptitude Test scores are normally distributed, with mean 500 and standard deviation 100. (a) What percentage of the scores are above 550? (Answer: 0.4085) (b) Approximately what score puts someone in the top 10-percent? (Answer: 629)