1.On a test the mean is 75 and the standard deviation is 5.

Question

A. What is the probability that a randomly selected score is higher than 80?
B. What percentage of the students scored higher than 80?
C. What percentage of the scores were less than 68?
D. What score separates the top 20% from the rest?
E. What score separates the bottom 15% from the rest?
F. If a set of 32 students are selected, what is the probability that the sample mean is less than 77?

Answer 1

A, B, C. Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z scores you've found.

D, E. Reverse process from the same table. Use the % to find the Z score, then insert into the formula to find the score.

F. For Distribution of means, Z = (score-mean)/SEm (Standard Error of the mean)

SEm = SD/√(n-1)

Use same table.

Answer 2

Here is a great normal distribution calculator
http://davidmlane.com/hyperstat/z_table.html

You can enter the data either directly or as z-scores.

Answer 3

Thanks

Answer 4

population scores with a mean (u) of 200 and a standard deviation (Q) of 10 wiht a normal distribution what score would cut off 5 percent os scores