Question

6. A first year medical school class (n = 200) took a first midterm examination in human physiology. The results were as follows: Mean= 65, Standard deviation = 7). Explain how you would standardize any particular score from this distribution, and then solve the following problems:

a. What Z score corresponds to a test score of 40?
b. What Z score corresponds to a test score of 50?
c. What Z score corresponds to a test score of 60?
d. What Z score corresponds to a test score of 70?
e. How many students received a score of 75 or higher?

Answer 1

a. To standardize a score, you subtract the mean of the distribution and divide by the standard deviation. So for a test score of 40:

Z = (40 - 65) / 7 = -5.71

b. For a test score of 50:

Z = (50 - 65) / 7 = -2.14

c. For a test score of 60:

Z = (60 - 65) / 7 = -0.71

d. For a test score of 70:

Z = (70 - 65) / 7 = 1

e. To estimate the number of students who scored 75 or higher, you can use a Z table to find the proportion of scores that fall above a certain Z value and multiply that by the total number of students. The Z score corresponding to a score of 75 is:

Z = (75 - 65) / 7 = 1.43

From a Z table, you can see that approximately 0.0888 or 8.88% of the scores fall above Z = 1.43. So an estimate of the number of students who scored 75 or higher would be:

200 * 0.0888 = 17.76 ≈ 18 students