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. In order to pass the Mathematics Pre- Test, a student must score 140 points or more. If 360 freshmen took the pre-test last fall, how many failed?
First, we need to find the z-score for a score of 140:
z = (140 - 120) / 20 = 1
Using a z-table, we can find the probability of scoring below a z-score of 1, which is 0.1587. This means that the probability of scoring 140 or higher is 1 - 0.1587 = 0.8413.
Now we can find the number of students who passed the pre-test:
0.8413 x 360 = 303.87
Since we can't have a fraction of a student, we round down to 303. Therefore, the number of students who failed is:
360 - 303 = 57
302
I apologize for the error in my previous response. The correct answer is:
0.8413 x 360 = 302.88
Rounding down to the nearest whole number, we get:
302 students passed the pre-test.
Therefore, the number of students who failed is:
360 - 302 = 58.
So, 58 freshmen failed the pre-test.
To determine how many students failed the Mathematics Pre-Test, we need to calculate the number of students who scored less than 140 points. We can do this by finding the Z-score for a score of 140 points and then using the standard normal distribution table.
The Z-score formula is:
Z = (X - μ) / σ
Where:
Z is the z-score,
X is the raw score,
μ is the mean, and
σ is the standard deviation.
In this case:
X = 140,
μ = 120, and
σ = 20.
Substituting the values, we get:
Z = (140 - 120) / 20
Z = 20 / 20
Z = 1
Now, we need to find the area to the left of a Z-score of 1 in the standard normal distribution table. This area represents the proportion of students who scored less than 140 points.
Looking up the Z-score of 1 in the standard normal distribution table, we find that the area to the left is 0.8413.
Next, we calculate the number of students who scored less than 140 points by multiplying the area by the total number of students:
Number of students scoring less than 140 = 0.8413 * 360
Calculating this, we get:
Number of students scoring less than 140 = 302.68
Since the number of students must be a whole number, we round down to the nearest whole number. Therefore, 302 students scored less than 140.
To find the number of students who failed, we subtract the number of students who scored 140 or more from the total number of students:
Number of students who failed = Total number of students - Number of students who scored 140 or more
Number of students who failed = 360 - (360 - 302)
Number of students who failed = 360 - 58
Therefore, 58 students failed the Mathematics Pre-Test at Thomas Nelson Community College.