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Consider a binomial experiment with 4 trialsand p=0.31p=0.31. Find P(x=3)P(x=3).Select one:a. 0.0822b. 0.0963c. 0.0891d. 0.1038...

Question

Consider a binomial experiment with 4 trialsand p=0.31p=0.31. Find P(x=3)P(x=3).Select one:a. 0.0822b. 0.0963c. 0.0891d. 0.1038

Consider a binomial experiment with 4 trials and p=0.31p=0.31. Find P(x=3)P(x=3). Select one: a. 0.0822 b. 0.0963 c. 0.0891 d. 0.1038



Answers

Consider a binomial experiment with 20 trials and probability 0.45 of success on a single trial. (a) Use the binomial distribution to find the probability of exactly 10 successes. (b) Use the normal distribution to approximate the probability of exactly 10 successes. (c) Compare the results of parts (a) and (b).

All right. So we have a binomial experiment of huge files and a probability of success of 0.4. So let's make a try. Trey. Tree diagram. My apologies. So success and fail. And then for a second trial, we make four branches. Success fail, success fail. Now we noticed that our experimental outcome is gonna be success. Success, success fail, fail, success fail, fail. And we're also going to get our discreet variable X. This is to success is one success one success, zero successes. All right, with that done, let's do some probabilities. So first off, we want to find of one, and we find this by just doing the formula. So it's gonna be you choose one times the probability of success point for to the first power times 0.6 times two minus one to the two minus one power. And that's gonna be two times 0.4 times 0.6, which is zero going for eight now. For part C, you need to find problem, Bill. Sorry. Zero, which is choo choo zero time 0.4 thio First power times 0.6 Site not to the first power to the zeros power times 0.6 to the second power. And this becomes one times one times 0.36 So is there a 0.36 party? You want to find the probability two successes or off of two. So this is two shoes too. Time, 0.4 to the second power times 0.62 The two minutes two or zero power. So that's one time 0.16 times one. So zero 0.16 All right now, we need to find the probability of at least one success. And to do that, it's gonna be one minus probability. I'm no successes, which is gonna be one minus zero one minus 0.36 0.64 All right part. Oh, I'm gonna remind everyone we have two trials and our probability of success is 0.4. So now we need to find the mean variants and standard deviation. All right, the mean. It's just end times p. It's gonna be two times 0.4. So 0.8 The variance is N times P times one minus p, which is two times 0.4 times 0.6 0.4 times 0.6 is Job 24. Multiply that by two you get 0.48 and for the state of deviation, that's just square root of the variants. So we have the square root of 0.48 which is approximately 0.69 to eight.

Question number three for a phenomenal experiments. There are always two possible outcomes, which are referred to as a success or a failure. So the answer will be to outcomes. Sex is all figures.

Question number seven Given be off a equally 4.4. Hmm. Off the equal. 4.5. Be off. See Equal opening one. Question. Number eight. We can't use a binomial model toe ermine. Their probability because there are three possible outcomes, while a binomial model has only two possible outcomes. Question number be We can use a binomial model to remind the probability, because there are two possible outcomes. Assuming that a success is an outcome off type A and that the failure is an outcome off, not type A. So the insecurity. Yes, because 02 possible outcomes the probability of taxes. The probability of circus is the probability off the outcome of type E. So your feet equal 4.4.

In this problem, we have been asked to determine whether given probability experiment represents a binomial experiment. Now the probability experiment is that an experimental drug is administered to 100 randomly selected individuals with a number of individuals responding favorably recording. Now I know that for this to be a binomial probability experiment, They will need to satisfy four conditions. Now the first condition is that the experiment is performed a fixed number of times. That is, there will be a fixed number of trials here. The number of trials will be considered to be 100 because it is administered 200 randomly selected individuals. Hence it is fixed. The second condition is that the trials need to be independent and in this case the trials are independent. This is because whether or not one patient response favorably does not impact whether or not the second patient response favorite. Now the third condition is that for each other should be two mutually exclusive outcomes. One will be success. The other will be a failure. In this case there are two outcomes. One is that yes, the individual responds favorably and the other one is no. The individual does not respond favorite. Hence the third condition that there are to this joint outcomes is also satisfied. And the fourth condition is that the probability of success that is p is the same for all the trials, and in this case the probability does not change between the individuals, so it will remain the same. Hence all four conditions are satisfied, and thus the answer is that yes. But given probability experiment represents a binomial experiment.


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