Suppose the scores of students on an exam are normally distributed with a mean of 501 and a standard deviation of 72. Then approximately 99.7% of the exam scores lie between the integers
and
such that the mean is halfway between these two integers. Use the empirical rule.
so, what is the rule?
You have the mean and the std....
To find the range of scores that includes approximately 99.7% of the exam scores, we can use the empirical rule, also known as the 68-95-99.7 rule. According to this rule:
1. About 68% of the scores will fall within one standard deviation of the mean.
2. About 95% of the scores will fall within two standard deviations of the mean.
3. About 99.7% of the scores will fall within three standard deviations of the mean.
Since we know the mean is 501 and the standard deviation is 72, we can apply the third part of the empirical rule: approximately 99.7% of the scores will fall within three standard deviations of the mean.
So, we need to find the range within which three standard deviations lie from the mean. To do this, we can calculate:
Lower bound = Mean - (3 * Standard Deviation)
Upper bound = Mean + (3 * Standard Deviation)
Lower bound = 501 - (3 * 72) = 501 - 216 = 285
Upper bound = 501 + (3 * 72) = 501 + 216 = 717
Therefore, approximately 99.7% of the exam scores lie between the integers 285 and 717, such that the mean is halfway between these two integers.