Worked solution
Check the normal model against the possible mark range
An examination is marked out of 100 and taken by a large number of candidates. The mean mark is 72.1 and standard deviation 15.2. Give a reason why a normal distribution with this mean and standard deviation would not give a good approximation to the marks.
[2008/H1/7(a)]
CJC · Discussion · Question 2
Answer
About 3.32% of the proposed normal distribution is above the maximum possible mark 100.
Evaluate both impossible tails
Under the proposed model , the source gives and .
Relate the probabilities to the context
Marks must lie between 0 and 100. The model assigns about 3.32% of candidates marks above 100. The source describes about 3% of a large cohort as significant; that substantial impossible upper tail makes this a poor approximation. The tiny lower tail is also impossible, but is not the main objection.
Common mistakes
A large cohort does not remove the upper bound on marks.
Solution notes
Complete source prompt and both calculated tails retained, including its about 3% argument. Normal notation identified as the model being assessed, not an accepted model. No marks printed.