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

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.
$$\begin{array} { l l } \text { Students } & \text { Number of Tests } \\\hline 10 & 1 \\7 & 2 \\2 & 3 \\1 & 4\end{array}$$
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:

Proximity

The physical or psychological closeness between people, objects, or ideas, which can influence social relations and interactions.

Physical Nearness

The spatial proximity of one object or person to another, which can influence social interactions and relationships.

Social Connections

The relationships individuals have with others, which can provide emotional, informational, and practical support.

Loneliness

A subjective feeling of isolation or being alone, regardless of the amount of social contact or presence of others, often accompanied by sadness or discomfort.