Normal distribution

Question

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 25 days and a standard deviation of 6 days.

72% of all of these types of trials are completed within how many days? (Round your answer to two decimal places.)

Answer 1

72% is close to 68% where the empirical rule means 1 standard deviation from the mean =z =-1 to z=+1

72% is a little more than 68% so the z score is a little more than |1|

68% of the trial are completed within 25-6 to 25+6 or 19 to 31 days

for 72% the range is a little larger, maybe 18 to 32 days?

use z tables or a z calculator for a more precise accurate answer

72% corresponds to z=1.08 and -1.08

(x-25)/6 = +/-1.08

x = +/-6(1.08)+25 =25+/-6.48

x = 18.52 to 31.48 days when 72% of the criminal trials are complete