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Chapter 5: Problem 77

A jury is supposed to represent the population. We wish to perform a simulation to determine an empirical probability that a jury of 12 people has 5 or fewer women. Assume that about \(50 \%\) of the population is female, so the probability that a person who is chosen for the jury is a woman is \(50 \%\). Using a random number table, we decide that each digit will represent a juror. The digits 0 through 5 , we decide, will represent a female chosen, and 6 through 9 will represent a male. Why this is a bad choice for this simulation?

Short Answer

Expert verified
The proposed simulation is a bad choice because it does not accurately represent the desired 50% probability for each gender. The selected digits would result in a 60% chance for females and 40% chance for males, which does not follow the approximate 50% population distribution intended to be replicated.

Step by step solution

01

Understand the Numerical Representation

The selected digits, for simulation of jury, are broken up as: numbers 0-5 represent females and numbers 6-9 represent males. This selection means that out of 10 digits, 6 are assigned for females and 4 for males.
02

Evaluate the Percentage Representation

To check if this split appropriately represents the 50% gender probability, percentages need to be calculated. Females are represented by 6 out of 10 digits, so they have a \(60\%\) representation. Similarly, males, represented by 4 out of 10 digits, have a \(40\%\) representation.
03

Compare Results to Desired Distribution

On comparing the split obtained from the digits, \(60\% - 40\%\), with the desired split, \(50\% - 50\%\), we can observe that the two don't match. As a result, the proposed numerical representation does not adequately simulate a 50% chance for each gender.

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