SOLUTION: The grades of an examination are normally distributed with a mean of 75 and a standard deviation of 12. a) The students who score in the bottom 5% will be retested. What score doe

Algebra ->  Probability-and-statistics -> SOLUTION: The grades of an examination are normally distributed with a mean of 75 and a standard deviation of 12. a) The students who score in the bottom 5% will be retested. What score doe      Log On


   

Question 62748: The grades of an examination are normally distributed with a mean of 75 and a standard deviation of 12.
a) The students who score in the bottom 5% will be retested. What score does this represent?
b) The top 10% are to receive a special award. What score must be earned to receive the award?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The grades of an examination are normally distributed with a mean of 75 and a standard deviation of 12.
a) The students who score in the bottom 5% will be retested. What score does this represent?
Determine the z-value corresponding to the lower 5% of the standard normal
distribution. It is z=-1.645
Find the X value corresponding to this z-value using the formula
z=[X-mu]/sigma
-1.645=[X-75]/12
X=55.26
------------
b) The top 10% are to receive a special award. What score must be earned to receive the award?
Find the proper z-value. It is 1.2816
Find the corresponding X
1.28816=[X-75]/12
X=90.38
Cheers,
Stan H.