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:

Hormones

Chemical messengers produced by glands in the body that regulate various physiological processes, including growth, metabolism, and reproduction.

Regulation

A rule or directive made and maintained by an authority to regulate behavior, usually in the context of legal, professional, or institutional settings.

Specific Gravity

The weight or degree of concentration of a substance compared with that of an equal volume of another, such as distilled water, taken as a standard.