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Binomial

Binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each which yields success with probability p. A success/failure experiment is also called a Bernoulli experiment or Bernoulli trial. The binomial distribution is often used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution. When N is much larger than n, the binomial distribution is a good approximation, and widely used.

Typically the mode of the binomial distribution is equal to [(n + 1)p] where [] is the floor function. However, (n+1)p is an integer and p is either 0 now 1, then the distribution has two mode, (n+1)p and (n+1)p-1. Where p is equal to 0 or 1, the mode will be 0 and n correspondingly. There is no single formula to find the median for a binomial distribution, and it may even be non-unique.

If n is large enough, then the skew of the distribution is not too great. In this case, a reasonable approximation to B(n, p) is given by the normal distribution. The baic approximation can be improved in a simple way by using a suitable continuity correction. The basic approximation generally improves as n increases and is better when p is not near to 0 to 1.

The binomial distribution converges towards the Poisson distribution as the number of trials goes to infinity while the product np remains fixed. Therefore the Poisson distribution with the parameter can be used as an approximation to B(n,p) of the binomial distribution if n is sufficiently large and p is sufficiently small.

Binomial Distribution of Telephone Bill Outcome

Based upon past experience, 1% of the telephone bills mailed to households are incorrect. A sample of 20 bills is selected. p= probability of success= 0.01 n= number of trails= 20 q= probability of failure = 0.99 a. What is the

Need help ASAP on Integer/Binomial Programming Homework!!

Solve the linear programming models using either lp_solve (recommended, see linear programming tutorial) or excel solver (Google for details). Include mathematical models. 1. A company has 4 projects to be assigned among 3 employees. Find the assignment that minimizes the total time spent by the employees: Peter Mary

Binonomial Distribution

Can you please explain to me how to do this; I'm so lost. "As a quality engineer working on the Rangdo production line, you have determined that the probability of producing a defective part is 6%. You want to develop a plan to monitor the quality of this line. Your idea is to take a sample of 20 parts every hour and determ

Variance and the Standard Deviation

In San Francisco, 30% of workers take public transportation daily. a) In a sample of 10 workers, what is the probability that exactly three workers take the public transport daily? [Hint: It is a Binomial Distribution Problem.] f(3) = b) In a sample of 10 workers, what is the probability that at least three w

Solving a Binomial Distribution Question

Please help with the following problem. Provide step by step calculations. Looking for the steps to figuring out this problem. Should I use some form of a calculator? Is this a binomial distribution question? A student is taking a 10 question quiz. There are four possible answers to each question. The student decide

Binomial Distribution

Can the binomial distribution be used to model the number of rare events that occur over a given time period?

Robert Smith Case Study

3. Robert Smith of the "Merrill Lynch Pierce Fenner & Smith" families is engaged in full-time fundraising. He has been quite successful at this because he brings a very structured approach to the process: you ask people directly and quickly for money. You don't waste your own time and you don't waste their time. His view is

Binomial Expansion

By expanding the binomial in (see equation in attached file) and summing term by term, derive a formula for calculating the kth moment about the mean in terms of the kth and lower order moments about the origin.

Probability - Binomial, Normal

1. The Arizona State Office of Tourism Development compiles information about the scenic attractions visited by out-of-state vacationers. The office reports that 75% of out-of-state vacationers visit the Grand Canyon, 35% visit the Sunset Crater (Meteor Crater), and 20% visit both. What is the probability that an out-of-state va

Density Function (Poisson, Binomial)

(a) If X ~ Poisson ........, compute Mx(t). (b) Show that if Xn ~ Binomial {see attachment} then Mxm(t) converges to Mx(t) for every t, where X ~ Poisson .......

Use the normal approximation to the binomial without a correction for continuity.

Statistics show that 69% of all college seniors have a job prior to graduation. If a random sample of 65 recent college graduates is taken, approximate the probability that at most 44 have a job prior to graduation. Do this in the following two ways: a. Use the normal approximation to the binomial without a correction for conti

Probability and binomial distributions 20 point value

Acme plumbing supply just received a shipment of 5,000 stainless steel valves, but 50 regular steel valves were also sent. There is no way to tell the difference between the valves. A customer orders 5 stainless steel valves . What is the probability that one or more will be regular steel? What distribution will be used? What ar