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 DecisionConsider 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 0.30Q: What is the probability that two of the next three customers will make a purchase?

Example: Hourly WagesAccording 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 2003.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 moreb-) At most five workers earned wages of USD 10 per hour or morec-) Anywhere from 4 to 6 workers earned wages of USD 10 per hour or more

The Sales of Automobiles for 300 days0 automobile sold 54 days

1 automobile sold 117 days

2 automobile sold 72 days

3 automobile sold 42 days

4 automobile sold 12 days

5 automobile sold 3 days

Total: 300 days