Homework: Waiting for the jury Defendants often ask their attorneys (at least on

Question

Homework: Waiting for the jury Defendants often ask their attorneys (at least on TV) what it means that the jury is deliberating for so long. Suppose that deliberation time is normally distributed with a mean of 4 hours and a standard deviation of 1 hour for cases ending in conviction and a mean of 5.5 hours and a standard deviation of 90 minutes when acquittal results. Also, 86% of cases result in convictions. In a particular case, the jury has been out already for 6 hours, which is encouraging to the defense. What is the probability of acquittal? Hint: Use the normal curve within a tree problem.

Explanation / Answer

Acquittal : N(4,1)

Conviction : N(5.5,1.5)

P(Acquittal) = 0.14

X= time when decision is made

P(Acquittal | X>6) = P(X>6 | Acquittal). P(Acquittal) / P(X>6)

= P(X>6 | Acquittal). P(Acquittal) / (P(X>6 | Acquittal).P(Acquittal) + P(X>6|Conviction).P(Conviction)

= P(Z>(6-4)/1)*0.14/(P(Z>(6-4)/1)*0.14 + P(Z>(6-4.5)/1.5)*0.86) = 0.0228*0.14/(0.0228*0.14 + 0.1587*0.86) = 0.023

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