Example-1: An insurance company sells a 10,000 TRL 1-year term insurance policy at an annual premium of 290 TRL. Based on many year’s information, the probability of death during the next year for a person of customer’s age, sex, health etc. is Q: What is the expected gain (amount of money made by the company) for a policy of this type?

Example: 2 The College Board website provides much information for students, parents, and professionals with respect to the many aspects involved in Advanced Placement (AP) courses and exams. One particular annual report provides the percent of students who obtain each of the possible AP grades (1 through 5). The 2008 grade distribution for all subjects was as follows: AP Grade Percent a. ) Express this distribution as a discrete probability distribution. b. ) Find the mean and standard deviation of the AP exam scores for 2008.

Properties of the Binomial Probability Distributions 1- The experiment consists of a sequence of n identical trials 2- Two outcomes (SUCCESS and FAILURE ) are possible on each trial 3- The probability of success, denoted by p, does not change from trial to trial. Consequently, the probability of failure, denoted by q and equals to 1-p, does not change from trial to trial 4- The trials are independent.

According to a research only 5% of the cigarette smokers enter into a treatment program to help them quit smoking. In a random sample of 200 smokers, let x be the number who enter into a treatment program. A-) Explain why x is a binomial r.v. B-) What is the value of p? Interpret this value. c-) What is the expected value of x? Interpret this value.

Example :4 The Heart Association claims that only 10% of adults over 30 can pass the minimum requirements of Fitness Test. Suppose four adults are randomly selected and each is given the fitness test. Use the formula for a binomial random variable to find the probability distribution of x, where x is the number of adults who pass the fitness test. Graph the distribution.

According to a research one in every three women has been a victim of domestic abuse. Suppose we randomly sample 15 women and find that four have been abused a-) What is the probability of observing four or more abused women in a sample of 15 if the proportion p of women who are victims of domestic abuse is given as p=0.30? b-) Calculate the probability of observing four or more abused women in a sample of 15 if p=0.10

Example: Purchase Decision Consider the purchase decisions of the next three customers who enter the clothing store. On the basis of past experience, the store manager estimates the probability that any one customer will make a purchase is 0.30 Q: What is the probability that two of the next three customers will make a purchase?

Example: Hourly Wages According to a study in a certain city 50% of workers between the ages of 25 to 34 years were paid hourly rates of USD 10 or more in the year of Find the probabilities that among 10 randomly selected workers in this category; a-) At least five workers earned wages of USD 10 per hour or more b-) At most five workers earned wages of USD 10 per hour or more c-) Anywhere from 4 to 6 workers earned wages of USD 10 per hour or more