Question

about what percentage of the data lies within 2 standard deviations of the mean in a normal distribution?
47.5%
68%
95%
99.7%

Explanation:

Step1: Recall Normal Distribution Rules

In a normal distribution, the empirical rule (or 68 - 95 - 99.7 rule) states the percentage of data within \( k \) standard deviations (\( \sigma \)) of the mean (\( \mu \)):

• Within \( 1\sigma \): ~68%
• Within \( 2\sigma \): ~95%
• Within \( 3\sigma \): ~99.7%

Step2: Match with the Question

The question asks for the percentage within 2 standard deviations. From the rule, this is approximately 95%.

Answer:

95% (the option with "95%")