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: 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

The Sales of Automobiles for 300 days 0 automobile sold54 days 1 automobile sold117 days 2 automobile sold72 days 3 automobile sold42 days 4 automobile sold12 days 5 automobile sold3 days Total:300 days