What Is the Value of k in This Normal Distribution Problem?

[gillgill]

i am having trouble with this question...

On a test, the marks were normally distributed with a mean mark of 54 and a standard deviation of 9. If the number of students who received a mark less than or equal to k was twice the number of those who received a mark of 80 or better, then the value of k, correct to the nearest whole number, was...

 

[HallsofIvy]

What have you done? You can calculate the "standard" variable corresponding to x= 0: z= (80- 54)/9 and look up the probability in a table. (There's probably one in your textbook but http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/normaltable.html
has one on the internet.) That's not actually the "number of students who received a mark of 80 or better"- it is actually "1- (number of student who received a mark of 80 or less/total number of students)". But subtracting it from 1 gives "number of students who received a mark of 80 or better/total number of students" and doubling that will then give "number of students who received a mark of k or less/total number of students" and then use that with the table to determine the corresponding "z" and finally solve for "x" (which, to the nearest integer, is your "k").

 

[gillgill]

i figured it out...thanks...