For a normal distribution with mu = 400 and sigma = 100, what score separates th

Question

For a normal distribution with mu = 400 and sigma = 100, what score separates the top 40% of the distribution from the rest? a) 475 b) 525 c) 552 d) 425 The distribution of sample means (for a specific sample size) consists of _____. a) all the scores contained in the sample b) all the scores contained in the population c) all the sample mean that could be obtained (for the specific sample size) d) the specific sample mean computed for the sample of scores A population has mu =50 with sigma = 4. The distribution of sample means for samples of size n = 4 selected from this population would have an expected value of the mean of _____. a) 4 b) 80 c) 50 d) 20 The standard deviation of the distribution of sample means is called _____. a) the expected value of M b) the standard error of M c) the sample mean d) the central limit mean The distribution of sample means _____. a) is always normal b) is normal only if the population distribution is normal c) is normal only if the sample size is greater than 30 d) None of the other 3 choices is correct. When the sample size is less than n = 30 _____. a) the distribution of sample means will be approximately normal b) the expected value of the sample mean will be equal to the population mean c) the distribution of sample means will be approximately normal and the sample mean will equal the population mean d) None of the other 3 choices is correct. A population has mu = 80 with sigma = 4. The distribution of sample means for samples of size n = 4 selected from this population would have a standard error of _____. a) 1 b) 8 c) 4 d) 2

Explanation / Answer

12. Let x denote the number which seperates the top 40% from the rest then,

P(X<x) = .6   

P(Z<(x-400)/100) =P(Z<.25335) (from normal distribution tables)

then x gives 425

13.The distribution of sample means (for a specific sample size) consists of all the sample means that could be obtained for the specific sample size.

When a random sample is selected from a population, the sample mean is not expected to be exactly equal to the population mean. On average, the size of the difference between the sample mean and the population mean is predicted by the expected value.
As sample size increases, the standard error of M decreases.

14.we know that sample mean is an unbiased estimator of population mean . Since populatin mean is equal to 50 then expected value of the sample mean will be equal to 50 too

15.the standard deviation of the sample mean is called STANDARD ERROR

16. option is the last one i.e no option is correct. Distribution of sample mean folloes norml distribution if either of the following is satisfied-

–The population from which the sample is drawn is normal.

–The number of scores (n) in each sample is relatively large (n>30)

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