In a normally distributed set of data containing 12 658 scores, how many scores are expected to be more than two standard deviations away from the mean.
In a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. This means that about 2.5% of the data is expected to be more than two standard deviations below the mean, and about 2.5% of the data is expected to be more than two standard deviations above the mean.
To find out how many scores are expected to be more than two standard deviations away from the mean in a set of 12,658 scores, we can use the following formula:
Number of scores = (Percentage of scores / 100) x Total number of scores
Since we know that approximately 2.5% of the data is expected to be more than two standard deviations above the mean, we can calculate the number of scores as follows:
Number of scores = (2.5 / 100) x 12,658
Number of scores = 316.45
Therefore, we can expect approximately 316 scores to be more than two standard deviations above the mean in a set of 12,658 scores.
Answers & Comments
In a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. This means that about 2.5% of the data is expected to be more than two standard deviations below the mean, and about 2.5% of the data is expected to be more than two standard deviations above the mean.
To find out how many scores are expected to be more than two standard deviations away from the mean in a set of 12,658 scores, we can use the following formula:
Number of scores = (Percentage of scores / 100) x Total number of scores
Since we know that approximately 2.5% of the data is expected to be more than two standard deviations above the mean, we can calculate the number of scores as follows:
Number of scores = (2.5 / 100) x 12,658
Number of scores = 316.45
Therefore, we can expect approximately 316 scores to be more than two standard deviations above the mean in a set of 12,658 scores.