Let's use the example from the previous page investigating the number of prior convictions for prisoners at a state prison at which there were prisoners. We have a binomial experiment if ALL of the following four conditions are satisfied: The experiment consists of n identical trials.
Let X denote the number in the sample with no health insurance. What is the probability that exactly 3 of the 15 sampled have no health insurance?
Using the probability mass function for a binomial random variable, the calculation is then relatively straightforward: What is the probability that at most one of those sampled has no health insurance? That is, we need to find: What is the probability that more than seven have no health insurance?
Either way, it becomes readily apparent that answering this question is going to involve more work than the previous two questions. It would clearly be helpful if we had an alternative to using the binomial p.
The alternative typically used involves cumulative binomial probabilities.
For a discrete random variable X, the cumulative probability distribution F x is determined by: Now the standard procedure is to report probabilities for a particular distribution as cumulative probabilities, whether in statistical software such as Minitab, a TIsomething calculator, or in a table like Table II in the back of your textbook.
If you take a look at the table, you'll see that it goes on for five pages. Let's just take a look at the top of the first page of the table in order to get a feel for how the table works: In summary, to use the table in the back of your textbook, as well as that found in the back of most probability textbooks, to find cumulative binomial probabilities, do the following: Find the column containing p, the probability of success.
Let's try it out on our health insurance example. What do you get? Do you need a hint? We've used the cumulative binomial probability table to determine that the probability that at most 1 of the 15 sampled has no health insurance is 0.
For kicks, since it wouldn't take a lot of work in this case, you might want to verify that you'd get the same answer using the binomial p. What is the probability that more than 7 have no health insurance? What is the probability that exactly 3 have no health insurance?
Again, for kicks, since it wouldn't take a lot of work in this case, you might want to verify that you'd get the same answer using the binomial p. What is the probability that at least 1 has no health insurance? What is the probability that fewer than 5 have no health insurance?
We have now taken a look at an example involving all of the possible scenarios Have you noticed that p, the probability of success, in the binomial table in the back of the book only goes up to 0. What happens if your p equals 0. All you need to do in that case is turn the problem on its head!
Just change the definition of a success into a failure, and vice versa! That is, finding the probability of at most 3 successes is equivalent to 7 or more failures with the probability of a failure being 0.
Shall we make this more concrete by looking at a specific example? Example Many utility companies promote energy conservation by offering discount rates to consumers who keep their energy usage below certain established subsidy standards.
If ten residential subscribers are randomly selected from San Juan, Puerto Rico, what is the probability that at least four qualify for the favorable rates?
That is, the probability that at least four people in a random sample of ten would qualify for favorable rates is 0. If you are in need of calculating binomial probabilities for more specific probabilities of success psuch as 0.
You can then still use the methods illustrated here on this page to find the specific probabilities more than x, fewer than x,The expected value of this game is -2 (5/6) + 10 (1/6) = 0. In the long run, you won't lose any money, but you won't win any. Don't expect to see a game with these numbers at your local carnival.
Answer Selected Answer: (92) +.3 (90) +.1(95) Correct Answer: Evaluation Method Correct Answer Case Sensitivity Exact Match Question 36 5 out of 5 points Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame: Compute a 3-period moving average for period 4.
Looking back at Figure , we see that the expected value with the market research consultant report, named the expected value with sample information (EV w SI), is $58, The expected value without the sample information (EV w/o SI) (same as the expected value without perfect information) is $51, What is the expected value at node 4?
Round your answer to the nearest whole number. Show transcribed image text Consider the following decision tree. What is the expected value at node 4? Round your answer to the nearest whole number. Expert Answer. % (1 rating) Get this answer with Chegg Study.
Feb 08, · Consider the following data: x: 1 2 3 4 5 P(x): What is the expected value E(X). Round answer to one decimal attheheels.com: Resolved. - Binomial Distributions. Printer-friendly version. Unit Summary.
Try to figure out your answer first, then click the graphic to compare answers. Note: Y can only take values 0, 1, 2, , n, but the expected value (mean) of Y may be some value other than those that can be assumed by Y.