1. Binomial Distribution Introduction: Binomial distribution has only two outcomes or can be reduced to two outcomes. There are a lot of examples in engineering science as a binomial distribution such that: electrical switch, a born baby it will be either male or female, medical treatment can be classified as effective or ineffective, blood pressure normal or abnormal blood pressure.

2. Binomial Distribution Definition: A binomial experiment is a probability experiment that satisfied the following four requirements: 1.There must be a fixed number of trials. 2.Each trial can have only two outcomes or outcomes that can be reduced to two outcomes. These outcomes can be considered as either success or failure. 3.The outcome of each trial must be independent of one another. 4.The probability of success must remain the same for each trial.

3. Binomial Distribution Notations of Binomial distribution: P(S): the probability of success. P(F): the probability of failure. P: the numerical probability of success. Q: the numerical probability of failure. P(S) = p, P(F) = 1- p = q N: the number of trials. X: the number of success of trial.

4. Binomial Distribution The probability of success in a binomial experiment can be computed with this formula is:

5. Binomial Distribution Example 1: A coin tossed 3 times finds the probability of getting two heads. Solution: S: = HHH, HHT, HTH, THH, TTH, THT, HTT, TTT.

6. Binomial Distribution We can solve the above problem by binomial distribution as: 1.There are a fixed number of trial (Three times) 2.There are only two outcomes for each trial, heads or tails. 3.The outcomes are independent of one another [The outcome of one toss in no way affects the outcome of another toss] 4. The probability of a success (heads)=0.5 in each case.

7. Binomial Distribution Then we can use binomial distribution as: n = 3, X = 2, p=0.5, q = 0.5 then

8. Binomial Distribution Example 2: A survey found that one out of five Americans say that he or she has visited a doctor in any given month, if 10 people are selected at random, find the probability that exactly 3 will have visited a doctor last month. Solution:

9. Binomial Distribution Solution: N = 10, X = 3,

10. Binomial Distribution Example 3: A survey from teenage research unlimited found that 30% of teenage consumers receive their spending money from part time jobs. If 5 teenagers are selected at random, find the probability that at least 3 of them will have part time jobs.

11. Binomial Distribution Solution: To find the probability at least 3 have part time we should compute P (3), P (4) and P (5). P = 0.3, q = 1- 0.3 = 0.7, n = 5, X = [3, 4, 5]

12. Binomial Distribution Solution: P (at least 3 have part time jobs) = P (3) + P (4) + P (5) = 0.132 + 0.028 + 0.002 = 0.162

13. Binomial Distribution Example 4: A die is rolled 360 times, find the mean, variance and standard deviation of the number 4’s that will be rolled. Solution: N=360,

14. Binomial Distribution Solution:

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