1. For a sample selected from a population with a mean of µ=50 and a standard deviation of σ = 10:
a. What is the expected value of M and the standard error of M for a sample of n=4 scores?
b. What is the expected value of M and the standard error of M for a sample of n = 25 scores?

2. A population has a mean of µ = 80 and a standard deviation of σ = 10. If you selected a random sample of n = 25 scores, how much error would you expect between the sample mean and the population mean?

3. A population forms a normal distribution with a mean of µ = 75 and a standard deviation of σ = 20.
Sketch the distribution of sample means for samples of n = 100. What proportion of the sample means for n = 100 have values greater than 79? In other words, find p(M>79) for n = 100.

4. A normal-shaped distribution has µ=80 and σ = 15. Sketch the distribution of sample means for samples of n = 25 scores from this population. Compute the z-scores for M = 89 for a sample of n = 25 scores. Is this sample mean in the middle 95% of the distribution?

Solution Summary

This solution gives the step by step method for computing probabilities based on Z score.

... step method for the calculation of probability based on Z... normal distribution we have Z = . 10 Normal Probabilities. ... variable X X − 36 using Z score and from ...

... Calculation of probability based on Z score is given in the ... Graphs, normal probability distribution. ... We can calculate probabilities by the Z transformation and ...

... Then we can adopt Z transformation to compute the probabilities. ... Step by step method for computing probability based on Z score is given in the answer. ...

... Step by step method for computing probability based on Z score is given in the answer. Normal. Normal Probabilities. Common Data Mean 500 Standard Deviation 50. ...

... Please see the attached file. The solution gives the details of calculation of probability, Z scores and percentiles based on a normal distribution. ...

... It can be assumed that the population standard deviation is .5 ounces based on past ... Normal Probabilities. ...Probability for X<20 or X >0 P(X<20 or X >0) 1.3097. ...

... Step by step method for computing probability based on Z... corresponds to each of the following z-scores, z=1.00, z... 2. Find the z-score corresponding to a score...