Test scores on the
ACT exam are normally distributed with a mean of 211 and deviation of 4.8.
Using the 68-95-99.7 rule, find the percentage of ACT scores within 9.6 of the mean of 21.1, and 14.4 of the mean of 21.1
Mean ± 2 SD = 95%
Mean ± 3 SD = 99.7%
To find the percentage of ACT scores within a certain range of the mean using the 68-95-99.7 rule, you can follow these steps:
1. Calculate the lower and upper bounds of the range:
- For a range within 1 standard deviation of the mean, subtract and add the standard deviation to the mean.
- For a range within 2 standard deviations, subtract and add twice the standard deviation to the mean.
- For a range within 3 standard deviations, subtract and add three times the standard deviation to the mean.
2. Calculate the percentage of scores within the range:
- For a range within 1 standard deviation of the mean, approximately 68% of scores will fall within this range.
- For a range within 2 standard deviations, approximately 95% of scores will fall within this range.
- For a range within 3 standard deviations, approximately 99.7% of scores will fall within this range.
Now let's calculate the percentages based on the given information:
1. For a range within 9.6 of the mean of 211:
- Lower bound: 211 - 9.6 = 201.4
- Upper bound: 211 + 9.6 = 220.6
- This range is within 2 standard deviations, so approximately 95% of ACT scores will fall within this range.
2. For a range within 14.4 of the mean of 211:
- Lower bound: 211 - 14.4 = 196.6
- Upper bound: 211 + 14.4 = 225.4
- This range is within 3 standard deviations, so approximately 99.7% of ACT scores will fall within this range.
Therefore, approximately:
- 95% of ACT scores will fall within 9.6 of the mean of 211.
- 99.7% of ACT scores will fall within 14.4 of the mean of 211.