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13)A random sample of 36 Is taken from large population with mean of 122 and SD of 15 Find the probability that the mean will be greater than 126_0.48506) 0 50480.0...

Question

13)A random sample of 36 Is taken from large population with mean of 122 and SD of 15 Find the probability that the mean will be greater than 126_0.48506) 0 50480.05480.5482

13)A random sample of 36 Is taken from large population with mean of 122 and SD of 15 Find the probability that the mean will be greater than 126_ 0.4850 6) 0 5048 0.0548 0.5482



Answers

A population has mean 12 and standard deviation $1.5 .$ a. Find the mean and standard deviation of $x-$ for samples of size 90 . b. Find the probability that the mean of a sample of size 90 will differ from the population mean 12 by at least 0.3 unit, that is, is either less than 11.7 or more than 12.3 .

So in this question, we are told that a population has mean 128 and standard deviation 22. And first we're asked to find the mean and standard deviation of the sample mean X, so the mean Of the sample mean, it's just the mean of the population, that's 1:28. And the standard deviation is basically the population standard deviation divided by the square root of 36, so that's approximately 3.67. Now, we are asked to find the probability that the mean of a sample of size 36, so we have our Mean and standard deviation of the sample, the rest from the probability that it will be within 10 units of the population means that is between 1 18 and 1 38. So we convert that to our standard normal random variable, so we get Between -2.72 And 2.72. And that basically gives us .9967 -1033, And the probability is .9934.

So in this question, we're told that a normally distributed population has a mean of 25.6 and a standard deviation of 3.3. So we know the population is normally distributed, And whereas to first find the probability that a single randomly selected element of X exceeds 30, So because it's normally distributed, we can just use our standard normal distribution formula. So that's a disease, more than 30 25.6 over 3.3. So 30 -25.6, divided by 3.3 probability Z is more than 1.33 so that's one minus the probability that sees less than 1.33 Now from our table Z, less than 1.33. Looking at the values, You basically get 1.3, 0.9082, so You get 1 -0.90 heat two. So That gives us 0.0918 as a probability for part A in part B, we're asked to find the mean and standard deviation for samples of size nine, So the mean, it's just the population mean, which is 25.6. The standard deviation? Yes, 3.3 Divided by square root of nine, which is three, And that is 1.1. So we have party apart being now part C. Were asked to find the quality that the mean exceeds 30, so the sample mean exceeds 30. So in this case we're going to use our sample mean and standard division and probably dizzy Is more than 30 -25.6 over 1.1. So 30 -25.6 Over 1.1. That's four. So that's quality Z is more than four, which is one minus probability. Easy. Less than four. Policy. Less than force one. So the answer here is zero.

So in this question, were given a normally distributed population with men of 57.7 and a standard deviation, find the probability that a single randomly selected element X is less than 45. So this is a normally distributed population, so they can just convert that to our standard normal random variable, We have our population mean and standard definition. So that's probability oh z less than -1.052, which is .14 69 What? We were us to find the mean and standard deviation of the sample means that the mean of the sample mean is the population means Which is 57.7. The standard division is 12.1 over the square root of simple size, Which is 3.025. Find the probability that the mean of a sample of size 16 is less than 45, probability that the means of the sample is less than 45. So we take the sample means for for five minus 57 point 7/3 57.0.25 Which is equal to probably it easy, less than -4.19 that is zero.

So in this question we are told we were given a simple random sample size and 36 obtained from a population with mean 64 and standard deviation 18 for us to describe the sampling distribution of the mean of the sample means. So the sampling distribution is approximately normal because we do have a large enough sample size, it's approximately normal with the simple mean of the mean of the sampling distribution equal to the population mean. And the standard deviation he calls to 18 over route 36 is three. So we have our answer to a Now in beaver asked for the probability That the sample mean is less than 62 0.6. So we convert this to our Z distribution. So we have z less than 62.6 -64 over the standard deviation. So that's probability easy, less than minus 0.47, that gives us .31924 part. Mhm. Now in part C were asked for the probability that Access more than articles to 68.7. So converting that we basically have probability that Z is more than or equals to 1.57, which is one minus probability, sees less than 1.57, 1 -1 -9418. Just .058 two, That's our answer to part. See now in party were asked for the probability That access between 59.8 and 65.9. So converting that we have the probabilities. See yes, between the values .63 and -1.4. That's basically the probability that sees less than this 0.7357 minus the probabilities. It's less than this, 08 78 and that gives us .6 five 49. And so we have the answers.


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