Suppose we have a normally distributed dataset with 50000 sc

Suppose we have a normally distributed dataset with 50,000 scores. We compute the mean and SD and find mean = 31, and SD = 2.5.

The following general statements are made:

1) Close to 6000 scores are in the low to mid 40’s

2) Close to 25000 scores are higher than 30

3) Close to 8000 scores are lower than 27

4) Close to 15000 scores are in the mid to upper 30’s

Is there a way to determine if the statements are true, false, likely true, or likely false? Please explain!

Work on one and leave the rest for other students.

Solution

With the given information that a normally distributed dataset has 50,000 scores and mean = 31, and SD = 2.5, a statement like 1) Close to 6000 scores are in the low to mid 40’s can not be verified at all.

Thus, the general statements made are utterly false.