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Statistics - Normal distribution

16. For a normal population with mean=50 and standard deviation=10, what is the probability of obtaining a sample mean greater than 52 for each of the following sample sizes
n=5 _________________%
n=10 _________________%
n=50 _________________%
n=100 _________________%

An assessment of optimism forms a normal distribution with mean=75 and standard deviation=15. If a random sample of 25 people is selected and the mean score is computed for this sample, then

17. What are the expected values for the mean and standard error of the distribution of sample means ?
mean_______ and Standard Deviation_______

18. Of all the possible sample means, what proportion of the sample means will be greater than 82?
19. What proportion of sample means will be less than 70?
20. What proportion of sample means will be within 3 points of the population mean, i.e., between 72 and 78?


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Solutions to the posted problems are given in the attached solution file with step by step instruction so that it helps students to understand the procedure to be followed for working out such type of problems.