At Thomas Nelson Community College, the Pre-Test for Mathematics has 200 points on the test. The mean is 120 and the standard deviation is 20. What is the approximate percentage of students that scored below 100 points?
We can use the z-score formula to find the percentage of students that scored below 100 points:
z = (x - μ) / σ
where x is the score we're interested in (100), μ is the mean (120), and σ is the standard deviation (20).
z = (100 - 120) / 20 = -1
Using a z-score table or calculator, we can find that the percentage of students that scored below 100 points is approximately 15.87%.
To find the approximate percentage of students that scored below 100 points, we need to use the Z-score formula and then look up the corresponding value in the standard normal distribution table.
The formula for calculating the Z-score is:
Z = (X - mean) / standard deviation
In this case, X is the score of interest, the mean is 120, and the standard deviation is 20.
So, to find the Z-score for X = 100:
Z = (100 - 120) / 20
Z = -20 / 20
Z = -1
We find that the Z-score for X = 100 is -1.
Next, we need to find the cumulative area to the left of the Z-score -1 in the standard normal distribution table.
Looking up the Z-score -1 in the standard normal distribution table, the cumulative area is approximately 0.1587.
Since the percentage is required, we need to multiply the cumulative area by 100:
Percentage = 0.1587 * 100 = 15.87
So, approximately 15.87% of the students scored below 100 points.
To find the approximate percentage of students that scored below 100 points, we can use the concept of the standard normal distribution.
First, we need to standardize the score of 100 using the formula for the z-score:
z = (x - μ) / σ
Where:
- x is the score of interest (100 in this case)
- μ is the mean (120 in this case)
- σ is the standard deviation (20 in this case)
So, plugging in the values, we get:
z = (100 - 120) / 20
= -20 / 20
= -1
Now, we need to find the corresponding area under the standard normal distribution curve for a z-score of -1. This area represents the percentage of students that scored below 100.
Using a standard normal distribution table or a statistical calculator, we can find that the area to the left of z = -1 is approximately 0.1587.
To convert this to a percentage, we multiply by 100:
0.1587 * 100 = 15.87%
Therefore, approximately 15.87% of students scored below 100 points on the Pre-Test for Mathematics at Thomas Nelson Community College.