A Statistics Professor Classifies His Students According to Their Gender

question 56

Essay

A statistics professor classifies his students according to their gender and the number of hours of paid work they do a week. The following table gives the proportions of students falling into the various categories. One student is selected at random.
Paid Work (hours/week) $$\begin{array} { | l | c | c | c | c | } \hline \text { Gender } & 0 & 1 - 8 & 9 - 16 & \text { Over 16 } \\\hline \text { Male } & 0.06 & 0.20 & 0.15 & 0.06 \\\hline \text { Female } & 0.12 & 0.18 & 0.20 & 0.03 \\\hline\end{array}$$ a. If the student selected is female, what is the probability that he works between 1 and 8 hours a week?
b. If the selected student works more than 16 hours a week, what is the probability that the student is male?
c. What is the probability that the student selected is female or does do any paid work or both?
d. Is gender independent of the number of hours of paid work done a week? Explain using probabilities.

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Definitions:

Gradually

In a slow, step-by-step process, often used to describe how changes or developments occur over time.

Approach-avoidance Conflict

A psychological conflict that occurs when a goal or event has both attractive and unattractive aspects, leading to ambivalence about pursuing it.

Lesser Of Two Evils

A choice between two undesirable options, where the chosen option is seen as the less harmful or problematic one.

Latin Root

The base of a word derived from Latin, from which the meaning and words in many modern languages are formed.