The scores on a chemistry test are normally distributed. Approximately 95 percent of the scores fell between 78 and 92. What is the standard deviation for this distribution?
how many std's away is the 2.5% boundary?
The mean is at (78+92)/2 = 85
To find the standard deviation for this distribution, we need to use the concept of the empirical rule, also known as the 68-95-99.7 rule. According to this rule, for a normally distributed dataset:
- Approximately 68 percent of the data falls within one standard deviation of the mean.
- Approximately 95 percent of the data falls within two standard deviations of the mean.
- Approximately 99.7 percent of the data falls within three standard deviations of the mean.
In this case, we know that approximately 95 percent of the scores fell between 78 and 92. This interval represents two standard deviations from the mean.
So, to find the standard deviation, we can calculate the distance between the mean and either of the interval endpoints by dividing the range (92 - 78 = 14) by two (since it represents two standard deviations):
Standard Deviation = (Upper Limit - Lower Limit) / 2
= (92 - 78) / 2
= 14 / 2
= 7
Therefore, the standard deviation for this distribution is 7.