Is it a binomial distribution?

Question

Surveying 12 jurors and recording whether there is a "no" response when they are asked if they have ever been convicted of a felony.

Answer 1

Yes.

Data often arise in the form of counts or proportions which are realizations of a discrete random variable. A common situation is to record how many times an event occurs in n repetitions of an experiment, i.e., for each repetition the event either occurs (a "success") or it does not (a "failure").

Binomial Experiment

More specifically, consider the following experimental process:

There are n trials.
Each trial results in a success or a failure.
The probability of a success, p, is constant from trial to trial.
The trials are independent.

An experiment satisfying these four conditions is called a binomial experiment. The outcome of this type of experiment is the number of successes, i.e., a count. The discrete variable X representing the number of successes is called a binomial random variable. The possible counts, X = 0,1,2, ..., n, and their associated probabilities define the binomial distribution, denoted by B(n,p).

Answer 2

a million.) n :- type of trials p :- danger of success on a given trial q = a million-p :- danger of failure on a given trial undergo in suggestions, for a sufficiently super pattern length, a binomial distribution could be approximated via a common distribution. we are able to apply here rule: If np > 5 and nq > 5, then the pattern length is satisfactorily super, and we are able to approximate via a common distribution. So calculate np and nq in each case, and see whether or no longer they're greater suitable than 5. 2.) First attempt whether np > 5 and nq > 5. If this holds, then a binomial distribution could be approximated via a common distribution: N(pq, npq) or N(pq, np(a million-p) ) the place np is the mean (?) and npq is the variance (?^2) of the traditional distribution. To calculate a z-score, use the formulation: z = (x - ?)/? Plug on your values for x (given interior the question), ? = pq, and ? = squareroot(npq) to get your answer. 3.) There are sixty 5 questions, so the type of trials n = sixty 5 Mike has a a million in 5 risk of answering each question wisely, so p = a million/5 = 0.2 x = 10 questions we would desire to locate the risk of answering decrease than 10 questions wisely: P(X<10) you will would desire to transform x = 10 right into a z-score making use of the comparable formulation as earlier: z = (x - ?)/? the place ? = pq, and ? = squareroot(npq) in case you probably did it wisely, you will desire to get: z = -0.93026 Then making use of your z-tables, locate P(Z

Answer 3

Start systematically writing down all possible results. Hopefully you won't need to write them all down before you see if the distribution looks binomial.