Question:easy
How much of the sample is included in 1.95 SD?
How much of the sample is included in 1.95 SD?
Show Hint
About 1.96 SD from the mean covers roughly 95% of a normal distribution.
Updated On: Jul 8, 2026
- 99%
- 95%
- 68%
- 65%
Show Solution
The Correct Option is B
Solution and Explanation
Step 1: Recall the standard normal curve landmarks.
For data that follow a normal distribution, fixed shares of the values sit within set distances from the mean, measured in standard deviations (SD).
Step 2: List the key ranges.
About 68% of values lie within $\pm 1$ SD, about 95% lie within $\pm 1.96$ SD (often rounded to 2 SD), and about 99.7% lie within $\pm 3$ SD.
Step 3: Match 1.95 SD to a range.
The figure 1.95 SD in the question is essentially the familiar 1.96 SD cut off, so it marks the boundary that holds about 95% of the sample.
Step 4: Rule out the rest.
68% belongs to 1 SD, not 1.95 SD. 99% needs a wider spread, close to 2.58 SD. 65% is not a standard landmark at all.
Step 5: Conclude.
So the share of the sample within 1.95 SD of the mean is 95%.
\[ \boxed{95\%} \]
For data that follow a normal distribution, fixed shares of the values sit within set distances from the mean, measured in standard deviations (SD).
Step 2: List the key ranges.
About 68% of values lie within $\pm 1$ SD, about 95% lie within $\pm 1.96$ SD (often rounded to 2 SD), and about 99.7% lie within $\pm 3$ SD.
Step 3: Match 1.95 SD to a range.
The figure 1.95 SD in the question is essentially the familiar 1.96 SD cut off, so it marks the boundary that holds about 95% of the sample.
Step 4: Rule out the rest.
68% belongs to 1 SD, not 1.95 SD. 99% needs a wider spread, close to 2.58 SD. 65% is not a standard landmark at all.
Step 5: Conclude.
So the share of the sample within 1.95 SD of the mean is 95%.
\[ \boxed{95\%} \]
Was this answer helpful?
0
