Verified answer

PROBLEM:

Suppose that a set of exam scores has a mean of 75 and a variance of 25. Assume that the exam scores are normally distributed. What is the probability that an exam score is between 75 and 77?

SOLUTION:

Step 1: Identify the parts of the word problem. The word problem will identify:

• The mean (average or μ) — 75

• Standard deviation (σ) — 5

Standard deviation is the square root of variance.

• X: the numbers associated with “between” — 75 and 77

Step 2: Figure out the z-scores and Find the area in the z-table. Plug the X values into the z value formula and solve. The μ (the mean), is 75.

NOTE: If a Z-score is 0, it indicates that the data point's score is identical to the mean score.

See the attached pictures for the z-table and the graph (illustration).

Step 3: Add the computed z-scores to get the probability or area between 0 and 0.4. You can also convert them in percent.

ANSWER:

• The probability that an exam score is between 75 and 77 is 0.15542.