See the attached file.

16. For a normal population with mean=50 and standard deviation=10, what is the probabilityof obtaining a sample meangreater than 52 for each of the following sample sizes

n=5 _________________%

n=10 _________________%

n=50 _________________%

n=100 _________________%

An assessment of optimism forms a normal distributionwith mean=75 and standard deviation=15. If a random sampleof 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 errorof 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?

_________________%.

Solution(1)

Required probability = …

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