29.6 and & = 24.9. You intend to draw population of values has a normal distribution witfollo Please answer the following questions, and show your answers to ra...

Find the indicated probability and determine whether the given sample mean would be considered unusual. If convenient, use technology to l the probability. For a sample of $n=45,$ find the probability of a sample mean being greater than 551 when $\mu=550$ and $\sigma=3.7$

In problem 15. We have a distribution with mean equals 53 new equals 53 and the standard deviation equals 21 sigma equals 21. From this distribution or from this population, we will take a random sample of size 49 then and equals 49 as a random sample from the population and them some assembling distribution of X board. Somebody distribution will be approximately will follow a normal distribution with me and a standard division. As long as we have relatively large sample and equals 49 then assemble distribution will be approximately normal. So the sampling distribution will follow a normal distribution with a mean of the same mean of the population which is 53 and a standard division of or standard error, which equals the population Standard division divided by the square root of the sample size. Then it's 21 divided by the square root 49 and this is a normal distribution annotation. You're right here. The variance. This means the answers of our problem is the first answer is normal distribution with a block symmetry will be approximately normal, with a mean the mean of the sampling. Distribution equals the same mean of the population? 53 and the standard deviation for the standard error equals 21. Divided by square root of 49 which is 21 divided by seven will be three. These are the final answers of our problem.

So in this question, were given a population with mean 557 standard deviation 35 were asked to find the mean and central division of the simple means, so mean of the sample, mean is 557. The standard deviation of the sample mean is population standard deviation over The square root of the simple size of squared of 15 35. Over answer is basically four 94 97 So we have our answer to a Now in beer us probably that the mean of a sample of size 50, so the assemble mean will be more than 5:17. So that's probably it is easy. It's more than the standard normal random very book. So we're going to get published easy, more than So we take 5 70 minus 557 Divided by 4.9497. See is more than 2.6. Kareen, that's one- The probability is is less than 2.63. So, from our table For 2.63, we're basically going to get 0.99 5 7. So 1 -0.9957 gives us 0.0043.

So in this question, we are told that random samples of size 64 are drawn from a population With me in 32 and standard deviation five, We're asked to find first the sample mean, which is equal to the population means Which is 32. And then we're also asked to find the sample standard deviation, which is the population standard deviation divided by square root, and That's five over. Route 64, which is five over Yeah, That's .625 as the sample standard deviation.

So in this question, we're told that a population has a mean of 48.4 and a standard deviation of 6.3. And first we're asked to find the mean and standard deviation of the sample mean. So that's the the mean is just the population mean, which is 48.4. And the standard deviation of the sample mean is san traditional population divided by square root and which is basically six point 3/8 And that is .7875. Now, we're asked to find the probability that the mean of a sample of size 64 will be less than 46.7. So we have probability standard normal random variable is 46.7 minus 48.4 over .7875. So that's probability is the less than -2.16, Which is 0.0154.