A teacher keeps data on students tabulated by performance and gender of the students. The data is on a computer disc but unfortunately some of it is lost due to a technical glitch. Only the following data could be recovered:
| Gender | Performance | Total | ||
| Average | Good | Excellent | ||
| Male | - | - | 10 | - |
| Female | - | - | - | 32 |
| Total | - | 30 | - | - |
An expert committee was formed which decided that the following facts were self-evident: half of the students were either excellent or good; 40% of the students were female; one-third of the male students were average.
What is the proportion of male students in the good category?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.73
First find how many of the 30 good students are male; the proportion asked is the male share of the Good category.
Total and male students (32 females are 40% of all students):
\(\displaystyle \text{Total}=\frac{32}{0.40}=80\)
Male \(=80-32=48\)
Male good students (one-third of the males are average; 10 males are excellent):
Male average \(\displaystyle =\frac{48}{3}=16\)
Male good \(=48-16-10=22\)
Proportion of the Good category that is male:
\(\displaystyle \frac{22}{30}=0.733\ldots\approx\) 0.73