A Statistics Professor Classifies His Students According to Their Gender

question 59

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:

Risk Factor

Any attribute, characteristic, or exposure that increases the likelihood of developing a disease or injury.

Testicular Cancer

A type of cancer that originates in the testicles, the male reproductive glands; it is one of the most treatable and curable cancers when detected early.

White Men

A demographic group defined by race (white) and gender (male), often examined in socio-political and cultural contexts.

Black Men

Refers to male individuals of African descent or who identify with the Black racial and cultural group.