Question 1127107: If the results on a nationally administered introductory statistics exam is normally distributed with a mean of 90 points and a standard deviation of 10 points, determine the following:
a.Describe the graph of this distribution (if you can do so, produce an electronic sketch of the graph to the right, otherwise adequately describe the distribution graph through its shape and horizontal scale values.)
b.Find the z-score for a single exam that had 95 points. Then find the z-score for one with 72 points.
c. If x represents a possible point-score on the exam, find P(x > 109).
d.Find P(75 < x < 110) and give an interpretation of this value
e. What is the minimum number of points one must score on this exam if they want to be in the top 12% of all the scores?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z=(x-mean)/sd
the mean will be 90 with 1,2,3 sd s to the left at right at 60,70,80 and 100,110,and 120
z for 95 is +0.5
z for 72 is -1.8
P(x>109) is probability z>1.9, which is 0.0287
this is z between -1.5 and 2, which is from the table or calculator 0.9104
There is a 91% chance that a score will be between 75 and 110 if picked randomly
z is +1.17
z*sd=11.7
the score would be 101.7 for the minimum
|
|
|
