Answer:
- The mean, median and modal students' grades are all grade 70.
- The degree of spread of the grades about the mean grade is in grade value of the standard deviation, 15.
- Half of the class score grade 70 and beyond and half of the class also score grade 70 and below.
- 68% of the class score between grade 55 and 85.
- 95% of the class score between grade 40 and 100.
Step-by-step explanation:
If the normal distribution curve of the students' grades has a xbar = 70, and a σ = 15, it translates that the mean, median and the modal student grade is 70 because a normal distribution is that symmetric about the center of the distribution and the spread of the grades away from grade 70 is in grade scores of 15, the standard deviation.
It also directly mean that half of the distribution exist at grade 70 and above and the other half exists at grade 70 and below.
The empirical rule also explains further that 68% of the distribution exists between one standard deviation of the mean, that is;
68% of the distribution exists between (70±15) = (55, 85)
95% of the distribution exists between two standard deviations of the mean.
[70±(2×15)] = (40, 100)
Hope this Helps!!!
