If the data reflects the standard normal distribution,what is the percentage of the data with z-scores between -2 and 2 ?
(A) $92.2 \%$
B $90.83 \%$
C $95.44 \%$
D $98.18 \%$
Answer
\(\boxed{95.45\%}\) is the final answer, which is approximately equal to the given option C $95.44\%$.
Step 1 ：The z-score is a measure of how many standard deviations an element is from the mean. In a standard normal distribution, about 68% of the data falls within one standard deviation of the mean (that is, between -1 and 1), about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.
Step 2 ：Therefore, the percentage of the data with z-scores between -2 and 2 should be about 95%.
Step 3 ：Using the cumulative distribution function (CDF) for a standard normal distribution, we find that the CDF at 2 is approximately 0.9772 and the CDF at -2 is approximately 0.0228.
Step 4 ：The percentage of the data between -2 and 2 is then given by the difference between these two values, which is approximately 0.9545 or 95.45%.
Step 5 ：\(\boxed{95.45\%}\) is the final answer, which is approximately equal to the given option C $95.44\%$.
