Question

Desert Dunes High School has two mathematics classes for each year. One class is a standard class containing students who possess standard mathematical ability. The other class is an advanced class containing the all-round brightest students in each year. Due to time tabling issues at the school, the students in the advanced class are selected based on their abilities in both English and mathematics (thus forming two advanced classes in one).
The grades obtained by students in the standard mathematics class range from very low to very high. Most students gain marks between 60% and 70%, with an average mark of 65%. On rare occasions a student may severely fail, in which case this student is kept back a year. On similarly rare occasions a student may obtain a mark of over 90%, in which case this student is moved up to the advanced class.

The grades obtained by students in the advanced class vary substantially between those students who are in the class because of their mathematical ability and those who are in the class because of their English ability. Most of the mathematically inclined students gain marks between 90% and 100%, with an average of 95%. Most of the students who are talented at English gain marks between 50% and 60%, with an average of 55%.

Out of the standard and advanced classes, it would be more reasonable to model the grades of the ADVANCED or STANDARD mathematics class with a normal distribution????

Answer 1

Answer:

It is more reasonable to model the standard class with normal distribution

Step-by-step explanation:

- Standard Class:

 The range of grades/marks obtained seems normally distributed with a reasonable average of 65% and covering the entire spectrum. Since most of the students score around average 65% the bump of normal bell curve is well situated about the mean.

- Advanced Class:

 The range of grades/marks obtained seems concentrated at around 2 means one for the students with higher ability of mathematics and one for the students with lower ability of mathematics ( Higher for english ). The mathematics abled score in the upper percentile while the English abled score in the mid-lower percentile. The deviation of average scores for is large enough to make this a bimodal distribution rather than a normal distribution. However, there's strong correlation between excelling in one academic subject and excelling in another.

Conclusion:

It is more reasonable to model the standard class with normal distribution