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Find the = mean and the standard deviation ofthe sampling distribution ofx for n 102.The sampling distribution offis...

Question

Find the = mean and the standard deviation ofthe sampling distribution ofx for n 102.The sampling distribution offis

Find the = mean and the standard deviation ofthe sampling distribution ofx for n 102. The sampling distribution offis



Answers

Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. $n=84, p=0.65$

This question asks us to find the mean variance and standard deviation of a binomial distribution. We're told that the parameters of this distribution are that we have 124 trials and a probability of success equal to 0.26 So and is 1 24 and P is 0 26. Let's start with the mean, which we right, as the Greek letter mu mean, is going to be equal to end times p or the number of trials, times of probability of success. In this instance, it will be 1 24 times 0.26 which is equal to 32.24 So this is the mean of our binomial distribution. Now let's take a look at the variance we write. Variance as Sigma squared in various is equal to end times P. Times Q. Now we don't have AH value for Q Given, but it's something that we can find. Q is just the probability of failure. So the opposite of P, which means Q will always be equal to one minus p. If we subtract 0.26 from one will find that Q is equal to zero point 74 So any times p times Q in this instance is going to be 1 24 times 0.26 times 0.74 And when we plug this into a calculator will get that our variance is 23.8576 And finally, now we want to find our standard deviation are standard deviation is just the square root of our variants. That's all we need to do is so we're gonna take the square root of that number. We just found 23.8576 and we'll find that our standard deviation is about equal to four point eight eight. So these are your final answers. We found them mean the variants and the standard deviation of this distribution, and that was that.

This question asked us to find the mean variance and standard deviation of a binomial distribution. We're told that this distribution has the parameters and equals 316 at its 316 trials per experiment, and that P, or the probability of success, is equal to 0.82 Let's start with finding the mead, which be right, as the Greek letter you for binomial distributions. The mean is equal to N Times P now here and is 3 16 and P is equal to 0.2. So quick plug into a calculator finds that the mean of this distribution is 259.12 2 59 12 So moving on to the variance now the variance has a similar formula that we need. One more thing. Variants is going to be any times. P Times Q. Now what is cute? We don't have that parameter listed well. Q is just the probability of failure. So it's the opposite of P, which means that Q will always be equal to one minus p in this case one minus 0.82 which is just equal to 0.18 So when we multiply all these together we have our number of trials are probability of success and our probability of failure. We'll get that our variance is equal to 4.46 point 6416 That is our variance for this distribution. And finally, we want to find our standard deviation in our standard deviation. Would you write? A sigma is just the square root of variance. So we just take the square root of the number we just found square to 46.6416 and we'll find that our standard deviation is equal to 6.83 And there we have it. We have found our mean are variants and our standard deviation for this distribution.

This question wants us to find the mean variance and standard deviation of a binomial distribution. We're told that the parameters of this binomial distribution are that and the number of trials is equal to 50 and p. The probability of success is equal to 0.4. Let's start with the mean which we call Mu the Greek letter you view we know for a binomial distribution is equal toe end times p the number of trials times the number of successes. In this case, that's gonna be 50 times 0.4. And when we do that multiplication, we find that Mu is equal to 20. Now the variance is looks similar, but in this time is gonna be n times p times Cute. Now we don't have a Q listed up here as one of our parameters, so we need to figure what what that is. Q. Is the probability of failure, and it's always equal to one minus p so we can do this. Quick. Calculation one minus 0.4 is, of course, 0.6, so Q is 0.6. That's the probability that an individual trial fails, and when we multiply all of these together we'll have Sigma squared is equal to 50 times 0.4 times 0.6, which is equal to 12. And that is our variance. We have a variance of 12 and then we want to find our standard deviation under standard deviation is just the square root of our variants. So it's gonna be the square root of 12 which we can plug into a calculator and find is about equal to 3.46 So these air your final answers. We have a mean of 20 variance of 12 and a standard deviation of about 3.46

In this question, we are given the poverty function Our X equals no point to for X equals not 123 on before. So we are asked to find the mean and standard deviation. So the first step is to dio our property distribution tables. We are no one to hey wonderful. When we get told, it's no point to went to Teoh went to and not point to stuff. It's nice and easy. The next room we need to do is X he exit. We're gonna times are probability of X which is not 20 for all of them and by the value of X itself. So for the 1st 1 we're times in nor point to buy zero So we get zero 2nd 1 time to North point to buy one which is no point to no no point to about two, which is full no point you by three which is six and no 60.2 times four which is ain't on Then the way we get the main is to some all these together. So every animal together we get to not to is me which is on me I'm just gonna put less some of X P x is a reminder of how we got that. So if we do total so the next thing we need to dio is doomed. Ex spread P X so x zero squared is still zero and zero times. Anything is zero once where it is still one so that times not point to a store not point to. But now two squared is four of four times no point to there's no 0.8 three squared is nine. So no 90.2 times nine is now. One point ain't on four spread is 16 so one out of the North Point to buy 16 which is 3.2 on the total for that is not quick to note. 0.8 plus 1.8 plus 3.2, which gives us six. So we now need ah variation, which is the expectation of X. It's what, which is this Butthead and we need to take from that expectation of X, which is our mean squared same. We're looking at six minus to squared. So that's six minus four, which is to on to get the standard deviation. We just need to do root off answer. So If we do, son deviation equal root of Arians equals route to Ruutu is actually an irrational number. So it will just keep going forever. So we'll just simplify to one distal place, which is 1.4. So they haven't you mean is too on the standard deviation is 1.4.


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