A Teacher Finds That Final Grades in the Statistics Department

question 17

Essay

A teacher finds that final grades in the statistics department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following grades were recorded. Determine if the grade distribution for the department is different than expected. Use α = 0.01. $$\begin{array} { l | l l l l l } \text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \\\hline \text { Number } & 36 & 42 & 60 & 8 & 14\end{array}$$

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Definitions:

Expected Value

The predicted value of a variable, calculated as a sum of all possible values each multiplied by the probability of its occurrence.

Insurance Policy

A contractual agreement between an individual or entity and an insurance company, outlining the terms for the insurer to compensate the insured for specific losses in exchange for premiums paid.

Premium

An amount paid in addition to a standard price, often for insurance, or a higher or more privileged level of service or product.

Expected Value

A calculated average of all possible outcomes of a particular random variable, weighted by their respective probabilities.