The mean on a Advanced Algebra test was 78 with a standard deviation of 8. If the test scores are normal distributed, find the interval about the mean that contains 99.7% of the scores. Use the empirical rule.
The mean on a Advanced Algebra test was 78 with a standard deviation of 8. If the test scores are normal distributed, find the interval about the mean that contains 99.7% of the scores. Use the empirical rule.
Do you know the 68-95-99.7 rule? Approximately 68% of scores in normal distribution are within one standard deviation (34% on each side of the mean), 95% within ±2 SD, and 99.7% within ±3 SD.
The mean on a Advanced Algebra test was 78 with a standard deviation of 8. If the test scores are normal distributed, find the interval about the mean that contains 99.7% of the scores. Use the empirical rule.
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To find the interval about the mean that contains 99.7% of the scores, we can use the empirical rule, which states that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.
In this case, the mean is given as 78 with a standard deviation of 8. Therefore, we want to find the interval that contains 99.7% of the scores, which is three standard deviations above and below the mean.
To calculate the upper value of the interval, we add three standard deviations to the mean:
Upper value = Mean + (3 × Standard deviation)
Upper value = 78 + (3 × 8)
Upper value = 78 + 24
Upper value = 102
To calculate the lower value of the interval, we subtract three standard deviations from the mean:
Lower value = Mean - (3 × Standard deviation)
Lower value = 78 - (3 × 8)
Lower value = 78 - 24
Lower value = 54
Therefore, the interval about the mean that contains 99.7% of the scores is from 54 to 102.