the average of final exam is 64, the standard deviation is 7. If the teacher set a rule that 1/4 of students who receive the poor grades should stay after class. lower than what mark should the students stay in school?
does anyone know how to solve this?
http://davidmlane.com/hyperstat/z_table.html
I get below 50.3
my friend came out with the following solution.
P(Z<-0.675)=0.25
-0.675= (X-64)/7
but i'm kinda confused.
where did the 0.675 come from?
Good question; ask your friend. It makes no sense. See the link I posted.
To find the mark below which the students should stay after class, we need to calculate the cutoff score.
First, let's define the poor grades as scores below a certain threshold. Let's assume that the cutoff score is "x."
We know that the average final exam score is 64, and the standard deviation is 7. This means that x is "a certain number of standard deviations below the mean."
To find the number of standard deviations below the mean, we can use the z-score formula:
z = (x - mean) / standard deviation
Since we want to find the cutoff score, we can rearrange the formula:
x = mean + (z * standard deviation)
Now, we need to find the corresponding z-score for the 1st quartile. Generally, the 1st quartile corresponds to a z-score of -0.674, as it covers about 25% of the data below the mean.
So, using the formula above, we can calculate:
x = 64 + (-0.674 * 7)
x = 64 - 4.718
x ≈ 59.282
Therefore, any student who receives a mark below approximately 59.282 should stay after class.
Note: It's important to remember that the z-score used may vary depending on the specific percentage of students the teacher wants in the lower grades. In this case, we assumed the 1st quartile, which covers approximately 25% of the data.