Question

en the standard normal distribution shown below, which of the following is the area of the shaded region? each mark on the x-axis represents one standard deviation.
a. 50%
b. 60%
c. 68%
d. 85%

Explanation:

Step1: Recall Empirical Rule

The empirical rule for standard normal distribution states that about 68% of data lies within \( \mu \pm 1\sigma \), 95% within \( \mu \pm 2\sigma \), and 99.7% within \( \mu \pm 3\sigma \). Here, the mean \( \mu = 0 \), and the shaded region is between \( -1 \) and \( +1 \) (since each mark is 1 standard deviation).

Step2: Match with Empirical Rule

The area between \( -1\sigma \) and \( +1\sigma \) is approximately 68% according to the empirical rule. Now check the options: A is 50% (half of the total, but not the 1 - sigma range), B is 60% (incorrect), C is 68% (matches the 1 - sigma range area), D is 85% (incorrect).

Answer:

C. 68%