| 
  • If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

  • Stop wasting time looking for files and revisions. Connect your Gmail, DriveDropbox, and Slack accounts and in less than 2 minutes, Dokkio will automatically organize all your file attachments. Learn more and claim your free account.

View
 

statprob1

Page history last edited by PBworks 14 years, 3 months ago

Problem 1 of 3

 

Ron wrote a History test and a Mathematics test. His scores, along with the mean and standard deviation for his class, are listed below. Assume that the class marks are normally distributed.

SubjectRon’s ScoreMeanStandard Deviation
History
73
70
6.2
Mathematics
67
64
5.3

(a) On which test did Ron perform better in relation to the class? Justify your answer.

 

(b) What percentage of the class scored between 65 and 75 on the History test?

 

(c) If the top 18% of the class received an A or a B on the History test, determine the minimum mark for a B.

 

 

Solution

(a) We find which test Ron had the greater z score on:

 

The formula to find the z score is z=(x-µ)/ơ

 

__History__: (73-70)/6.2 = .483

__Math__: (67-64)/5.3 = .566

 

So Ron did better on the Math test in relation to the class because the z score is greater.

 

(b)We find the z scores of 65 (low) and 75 (high).

 

Low: (65-70)/6.2 = -.8

High: (75-70)/6.2 = .8

 

Now that we have the z scores, we can use Shadenorm (shows graph) or Normalcdf (just shows percentage) to find the percentage of the class that scored between 65 and 75:

 

Normalcdf(-.8,.8) = .576 = 57.6%

 

So 57.6% of the class scored between 65 - 75 on the history test.

 

(c)Here we use InvNorm. Since invnorm calculates the left side of the graph, we need to use the opposite (.82).

 

InvNorm(.82,70,6.2) = 75.67

 

So 75.7% would be the minimum mark to get a B on the History test.

 

 

Next Problem

Home

Statistics

Comments (0)

You don't have permission to comment on this page.