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:

Significant Influence

This term refers to the power to participate in the financial and/or operating policy decisions of another entity, but not control those policies. It is often quantified by owning 20% to 50% of the voting shares of the investee company.

Investee

The company whose stock is purchased by the investor.

Held-to-Maturity Investments

Investments in debt securities that a company has the positive intent and ability to hold until maturity.

Broker's Commissions

This term refers to the fees that brokers earn for facilitating transactions or services such as sales of securities, real estate, or insurance policies.