Question

How much of the sample is included in 1.95 SD?

• A. 99%
• B. 95%
• C. 68%
• D. 65%

Hint:

About 1.96 SD from the mean covers roughly 95% of a normal distribution.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks what percentage of observations in a normal distribution fall within about 1.95 standard deviations of the mean.

Step 2: Key Concept:
In a normal (Gaussian) distribution, fixed percentages of the data fall within certain multiples of the standard deviation around the mean. These are commonly remembered as:
\[ \text{Mean} \pm 1\ SD \approx 68\% \]
\[ \text{Mean} \pm 1.96\ SD \approx 95\% \]
\[ \text{Mean} \pm 3\ SD \approx 99.7\% \]

Step 3: Detailed Explanation:
The value 1.95 SD used in the question is essentially the same as the well known 1.96 SD cut off used for the 95% confidence range in a normal distribution. So about 95% of the sample values are expected to lie within this range around the mean.
68% corresponds to 1 SD on either side of the mean, not to 1.95 SD.
99% corresponds to about 2.58 SD on either side of the mean, which is a wider range than 1.95 SD.
65% does not correspond to any standard SD multiple used in normal distribution theory.

Step 4: Final Answer:
About 95% of the sample lies within 1.95 (practically 1.96) standard deviations of the mean.
\[ \boxed{95\%} \]