A Calculus Instructor Uses Computer Aided Instruction and Allows Students $$\begin{array} { c c } \text { Students } & \text { Number of Tests } \\\hline 10 & 1 \\7 & 2 \\2 & 3 \\1 & 4\end{array}$$

question 22

Essay

A calculus instructor uses computer aided instruction and allows students to take the midterm exam as many times as needed until a passing grade is obtained.Following is a record of the number of students in a class of 20 who took the test each number of times. $$\begin{array} { c c } \text { Students } & \text { Number of Tests } \\\hline 10 & 1 \\7 & 2 \\2 & 3 \\1 & 4\end{array}$$
a.Use the relative frequency approach to construct a probability distribution and show that it satisfies the required condition.
b.Find the expected value of the number of tests taken.
c.Compute the variance.
d.Compute the standard deviation.

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Definitions:

Moral Principles

Fundamental beliefs about what is right and wrong, which guide individuals’ behavior and decision-making processes.

Selflessness

Placing the needs and well-being of others before one's own interests.

Compassion

A deep awareness of and sympathy for another's suffering combined with the desire to alleviate that suffering.

Social Contract Stage

A phase in societal development where individuals agree to form a community or society under a set of shared norms, values, and rules for mutual benefit.