When grading using “the curve”, the percentages are as follows: A: Top 10% of scores B: Scores between P70 and P90 C: Middle 40% (scores between P30 and P70) D: Scores between P10 and P30 F: Bottom 10% of scores CLASS #1: Suppose that the exam grades for Class #1 are as follows: 35 44 46 47 48 51 54 55 55 57 57 58 59 60 60 60 60 61 62 64 68 69 70 72 73 75 75 77 82 85 µ = 61.3 standard deviation = 11.5 a) Using the mean and standard deviation above and the invNorm feature of your calculator, determine “the curve” cutoffs for the PK values listed above. (These are not standard deviations.) Round these test grade cutoffs to one decimal. Label them underneath the curve. Test Grades 0 ____ ____ ____ ____ 100 b) Use the one-decimal place cut-offs in the picture you created in part (a) to fill in the chart below with the new range of scores for each letter grade under this plan. Then, look at the 30 test grades and count how many test grades would fall in each letter grade based on the new scale. Letter Grade Range of Scores Number of Tests
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
When grading using “the curve”, the percentages
are as follows:
A: Top 10% of scores
B: Scores between P70 and P90
C: Middle 40% (scores between P30 and P70)
D: Scores between P10 and P30
F: Bottom 10% of scores
CLASS #1: Suppose that the exam grades for Class #1 are as follows:
35 44 46 47 48 51 54 55 55 57
57 58 59 60 60 60 60 61 62 64
68 69 70 72 73 75 75 77 82 85
µ = 61.3 standard deviation = 11.5
a) Using the mean and standard deviation above and the invNorm feature of your calculator,
determine “the curve” cutoffs for the PK values listed above. (These are not standard deviations.)
Round these test grade cutoffs to one decimal. Label them underneath the curve.
Test Grades 0 ____ ____ ____ ____ 100
b) Use the one-decimal place cut-offs in the picture you created in part (a) to fill in the chart below
with the new
and count how many test grades would fall in each letter grade based on the new scale.
Letter Grade Range of Scores Number of Tests
A _______ to 100
B
C
D
F 0 to ______
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