SOLUTION: Let us assume that the grades of 500 students are normally distributed with 𝜇=45 and standard deviation 𝜎=20. If the 20% of the students get excellent, what is the grade that

Algebra ->  Probability-and-statistics -> SOLUTION: Let us assume that the grades of 500 students are normally distributed with 𝜇=45 and standard deviation 𝜎=20. If the 20% of the students get excellent, what is the grade that      Log On


   

Question 1185779: Let us assume that the grades of 500 students are normally distributed with 𝜇=45 and standard deviation 𝜎=20. If the 20% of the students get excellent, what is the grade that determines the excellent? (What is 𝛸 value?)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
mean = 45
standard deviation = 20
number of students = 500

z-score = (x - m) / s

in this problem:

x is the number of students who get excellent.
m is the mean = 45
s is the standard deviation = 20

you are looking for the z-score that has 20% of the area of the normal distribution curve to the right of it.

that z-score will be equal to .8416 when rounded to 4 decimal places.

to find the raw score, use the z-score formula of z = (x - m) / s

in this formula, z = .8416, m = 45, s = 20

the formula becomes .8416 = (x - 45) / 20

solve for x to get:

x = .8416 * 20 + 45 = 61.832.

a score above that will be excellent.
only 20% of the students will get a score greater than that.