Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days.

(a) In words, define the random variable X.

(b) Find the z-score for a trial lasting 24 days.

(c) If one of the trials is randomly chosen, find the probability that it lasted at least 24 days.

(d) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (b), rounded to one decimal place).

Shade:Left of a value

Right of a value

Between two values

2 regions

(e) eighty-two percent of all trials of this type is completed within how many days?