Question

What are the possible durations of suspension for the given offense?

1) 60 days
2) 120 days
3) 180 days

Answer 1

The random variable X refers to the duration of a criminal trial in days, where X follows a normal distribution with a mean of 21 days and a standard deviation of 7 days. To find the probability that a trial lasted at least 24 days, one would calculate the Z-score for x = 24 and look up the probability in the standard normal distribution table. Sixty percent of the trials are completed within a duration slightly less than one standard deviation from the mean.

Step-by-step explanation:

Understanding the Duration of Criminal Trials

The question refers to a probabilistic scenario where the duration of a particular type of criminal trial follows a normal distribution. The random variable X represents the duration of these criminal trials, in days. Since the distribution is normal, we denote it with its mean (μ) and standard deviation (σ). Thus, X is distributed normally with X~N(21, 72).

To answer the student's query:

1. In words, the random variable X refers to the duration of a criminal trial in days.
2. As defined, X~N(21, 72), where 21 is the mean of the distribution and 7 is the standard deviation.
3. The probability that a trial lasted at least 24 days can be found by calculating the area under the normal curve to the right of x = 24. The Z-score corresponding to x = 24 is calculated by Z = (X - μ)/σ, after which we look up this Z-score in the standard normal distribution table to find the probability.
4. Using the 68-95-99.7 rule (empirical rule), since 60% of the trials are completed, we're looking for the duration within approximately 1 standard deviation from the mean since 68% is the total percentage within 1 standard deviation. The duration within which 60% of the trials are completed would be slightly less than one standard deviation away from the mean, which is 21 days (mean) minus 7 days (standard deviation).

While the exact calculation would require the use of a cumulative distribution function or a Z-table, the question is best understood and solved by applying basic principles of the normal distribution.