the score of an achievement test is given to 100000 students are normaly distributed with mean 500 and s.d 100.what should be the score of a student to place among him top 10% of all students
from the z-score table
the top 10% of students have scores that are
... approximately 1.28 s.d. above the mean
500 + (100 * 1.28)
Answer please
To find the score required to place among the top 10% of all students, we can use the z-score formula as follows:
Z = (X - μ) / σ
Where:
Z is the z-score
X is the score we want to find
μ is the mean (500 in this case)
σ is the standard deviation (100 in this case)
We need to find the z-score that corresponds to the top 10% of the distribution. To do that, we can use the z-table or a calculator.
The z-score that corresponds to the top 10% is approximately 1.28. This means that the score we are looking for is 1.28 standard deviations above the mean.
Now we can solve for X using the z-score formula:
1.28 = (X - 500) / 100
Multiply both sides by 100 to isolate X:
128 = X - 500
Add 500 to both sides:
X = 500 + 128
Therefore, the score a student needs to place among the top 10% of all students is approximately 628.
To determine the score required for a student to be in the top 10% of all students, we need to find the cutoff point at which 10% of the students have scored below.
Let's use the properties of a normally distributed dataset and the z-score formula to calculate this. The z-score measures the number of standard deviations an individual score is from the mean.
First, we need to find the z-score corresponding to the top 10% percentile. We can use a standard normal distribution table or a statistical calculator to find this value. The z-score corresponding to the 10th percentile is approximately -1.28.
Now, we can use the z-score formula to find the raw score needed to achieve this z-score:
z = (x - μ) / σ
In this formula, z represents the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
Rearranging the formula to solve for x, we have:
x = z * σ + μ
Substituting the given values into the formula:
x = -1.28 * 100 + 500
Calculating the equation, we find:
x ≈ 372
Therefore, a student would need a score of approximately 372 to place among the top 10% of all students.