1.A set of reading scores for fourth-grade children has a mean of 25 and a standard deviation of 5. A set of scores for sixth-grade children has a mean of 30 and a standard deviation of 10. Assume that the distributions are normal.

Do you think the distributions overlap much? Explain.

2. From the previous question, the percentage of fourth-graders who score better than the average sixth-grader would be

The percentage of the sixth-graders who score worse than the average fourth-grader would be

3. Under what condition would the answers for each blank in the previous question be equal if the means can't change?

I know I'll have to compute a z-score at some point here, or perhaps a confidence interval, but I am so confused since all they have given me are the means and standard deviations. I know the mean and standard deviation of a normal distribution is 0 and 1, respectively, but I am so lost as to where to go from there.

The next problem is the same sort of thing, I am just confused as to how to get a z-score for ten percent. The closest I can find on my z-score table is .1026, am I approaching this wrong?

4. A toy factory owner plans to give pay raises this year using a normal distribution. She will make the mean raise $1000 and the standard deviation $265. Basing this on worker productivity (toys constructed), the most productive 10% of employees will see a raise of at least how much?