Question

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 22 days and a standard deviation of 6 days. 72% of all of these types of trials are completed within how many days

Answer 1

25.5 days

Explanation:

Mean number of days (μ) = 22 days

Standard deviation (σ) = 6 days

Z-score for the 72nd percentile (according to tabulated values) = 0.583

The z-score for any number of days, X, is determined by:

`z=(X-\mu)/(\sigma)`

The value of X that is greater than 72% of the trial times is:

`0.583=(X-22)/(6)\\ X=25.5\ days`

Therefore, 72% of all of these types of trials are completed within 25.5 days.