assume that a set of test scores is normally distributes with a mean of 120 and a standard deviation of 25. use the 68-95-99.7 rule to find the percentage of scores greater tha 145
145 is one s.d. above the mean
68% of scores are in this range
34% are above the mean
50% of scores are below the mean
that leaves 16% of scores above 145
To find the percentage of scores greater than 145, we can use the 68-95-99.7 rule, also known as the empirical rule or the normal distribution rule. This rule states that for a normally distributed dataset:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
Given that the mean is 120 and the standard deviation is 25, we can calculate the range of scores within certain standard deviations of the mean.
To find the percentage of scores greater than 145, we need to calculate how many standard deviations away from the mean 145 is.
First, we subtract the mean from the value we are interested in: 145 - 120 = 25.
Next, we divide the result by the standard deviation: 25 / 25 = 1.
This tells us that the value 145 is 1 standard deviation above the mean.
According to the 68-95-99.7 rule, approximately 68% of the data falls within one standard deviation of the mean. Therefore, approximately 32% (100% - 68%) of the data falls outside of one standard deviation.
Since the value 145 is one standard deviation above the mean, the percentage of scores greater than 145 is approximately 32%.