Question

Problems 1-4 assume a normally distributed population with a mean = 48 and standard deviation = 5. Be sure to sketch the curve, include formulas & work, round appropriately, and circle your final answer.

1. What percent of the scores fall:

at or below 54?

at or above 40?

2. (6 points) What proportion of scores lie between:

31 and 48?

31 and 54?

3. (4 points) Suppose we took a sample of 5000 scores from this distribution.

Of those 5000 scores, how many would you expect to lie between31 and 48?

Of those 5000 scores how many would you expect to lie between 31 and 54?

4. If you select one person at random from this population and find his/her score on this variable to be 63 would you be surprised (yes/no)? Why/why not?

5. (4 points) Later in the semester we will focus on z-scores that capture the middle 95% of the distribution.
   1. Find the two z-scores that capture the middle 95% of the distribution. Be sure to show your work. (Hint: remember that the normal curve is symmetrical.)

What two z-scores would we use if we want to capture the middle 99% of the distribution?

Answer 1

If you select one person at random from this population and find his/her score on this variable to be 63 would you be surprised (yes/no)? Why/why not?

Ans: Surprised, because score 63 is fall outside of the 99% confidence interval.