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
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 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