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Population mean5.1Sample Mean 4,25 Sample Sum of Squares 46,25 Sample N = 12Estimated population variance- 4.20 Variance ol the distribution ol means 0.35 Slandard ...

Question

Population mean5.1Sample Mean 4,25 Sample Sum of Squares 46,25 Sample N = 12Estimated population variance- 4.20 Variance ol the distribution ol means 0.35 Slandard deviation ol the distribution of means (standard errar) 0.59 Signilicance level 0,05Ihore is only ono (-score cutoll; write "Mone' In Ine olher box) The posilive (-score cutoll Is Tho nogallve (-score cutolf (s

population mean 5.1 Sample Mean 4,25 Sample Sum of Squares 46,25 Sample N = 12 Estimated population variance- 4.20 Variance ol the distribution ol means 0.35 Slandard deviation ol the distribution of means (standard errar) 0.59 Signilicance level 0,05 Ihore is only ono (-score cutoll; write "Mone' In Ine olher box) The posilive (-score cutoll Is Tho nogallve (-score cutolf (s



Answers

A population has a mean $\mu=150$ and a standard deviation $\sigma=25 .$ Find the mean and standard deviation of the sampling distribution of sample means with sample size $n .$ $$n=50$$

Okay, so we're given that population has a mean you off 1 50 Standard deviation 25 on a sample size of 400. Gay. Since this, it's sample size is greater than 30. You can use the central limit serum to conclude that the distribution of sample means is approximately normal with the mean and standard deviation. Quote to mute. Thanks, Andi. Standard deviation inspire which is equal to signal over Groot on don't physical 21 50 onda 25 over the square. Root off 100 which is equal to 2.5, Uh

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

Okay, so in this question, were given that the population as mean for 50 standard deviation of 25 on a sample size of 2 50. Since the sample size is greater than 30 we can use to central Limit serum to conclude the distribution of sample means is approximately normal on toe have mean on standard deviation equal to I mean a vehicle to mu salivation. Be good signal or square on should give us 1 50 which was 25 over. Describe to 50 which is equal to 1.5 fleet week not.

All right guys. So for this one, and they do want us to find the population variance and population standard deviation. So let's go and get started. I want to go ahead. I want to head and typed all the numbers into a google sheet. You know the same thing with Excel, if you prefer that, or if you would like to do by hand, go for go for it and reference your textbook, for example. But here's how you do it on google sheet. First, of course, you type it on the data, then we're gonna do is this I'm going to open, I'm going to go on a different cell here and hit the equal sign on my keyboard and now I'm going to start typing invariance. But be careful here because I need to make sure I do population variance and that's right here, V A R p, the variance of a population there is what we got right after that. It's gonna open apprentices for me. I do need to highlight everything with my cursor to make sure that I get all those data points I hit enter and that's it. Okay, now I need to do the standard deviation. Standard deviation for population is S. T dev P and that's right here, S T D F P standard deviation of an entire population. I click on that and um I highlight all the stuff I need, I hit enter and I'm done. Perfect. Alright, A great way to check as well is the standard deviation should be the square to variance eight is the square to 64, so we're done.


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