A shaded area reprsents approximately 95% of the scores on a standardized test. If these scores ranged from 78 to 92, whic could be the standard deviation?
I don't know what area is shaded.
If it is symmetrical around the mean, then 95% of the scores are within a Z score of 1.96 in either direction. (Since it says approximate, you could round it off to 2.) The mean is (78+92)/2 = ?
Z = (score-mean)/SD
Insert the values and solve for SD.
To determine which of the given options could be the standard deviation, we need to consider the 95% range and the scores of 78 to 92.
First, calculate the mean (average) of the scores:
Mean = (78 + 92) / 2 = 170 / 2 = 85.
Next, calculate the range in terms of standard deviations. The range of approximately 95% of scores falls within 1.96 standard deviations from the mean.
Using the formula for the range in terms of standard deviations:
Range = Standard Deviation × 1.96.
Substituting the given range (92 - 78) into the equation:
14 = Standard Deviation × 1.96.
Now we can solve for the standard deviation:
Standard Deviation = 14 / 1.96 ≈ 7.14.
Therefore, the standard deviation could be approximately 7.14.
You can verify this calculation by considering the given range and the fact that it represents approximately 95% of the scores on the standardized test.