Download 7.5 Notes

7.5 Binomial Distribution
Properties of a Binomial Experiment
A binomial experiment consists of a sequence of trials with the following conditions:
1. There are a fixed number of observations called trials.
2. Each trial can result in one of only two mutually exclusive outcomes labeled success (S) and failure
(F).
3. Outcomes of different trials are independent.
4. The probability that a trial results in S is the same for each trial.
The binomial random variable x is defined as
X = number of successes observed when a binomial experiment is performed.
The probability distribution of x is called the binomial probability distribution.
A. FINDING PROBABILITY FOR A BINOMIAL DISTRIBUTION:
FORMULA SHEET →
B. FINDING THE MEAN AND STANDARD DEVIATION FOR A BINOMIAL DISTRIBUTION
The mean value and the standard deviation of a binomial random variable are, respectively,
 x  np
FORMULA SHEET →
and
 x  np1  p 
What is the probability it will land on exactly 13 heads?
On average, how many flips will result is a heads?
What is the standard deviation of the distribution?
What is the probability it will land on heads no more than 5 times?
What is the probability it will land on heads at least 10 times?
What’s the probability it will land on heads between 8 and 15 times?
READ THE FOLLOWING FOR HOMEWORK:
A. Geometric Distributions
Suppose an experiment consists of a sequence of trials with the following conditions:
1. The trials are independent
2. Each trial can result in one of two possible outcomes, success or failure.
3. The probability of success is the same for all trials
A geometric random variable is defined as
x = number of trials until the first success is observed (including the success trial)
The probability distribution of x is called the geometric probability distribution.