Question

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. a. The duration of a criminal trial b. X ~ _N____(___21__,__7___) c. If one of the trials is randomly chosen, find the probability that it lasted at least 24 days. Sketch the graph and write the probability statement.

Answer 1

0.33411

The probability that a particular criminal trial lasted atleast 24 days is 0.33411

Explanation:

The random variable X is normally distributed with a mean of 21 and standard deviation of 7

;

X ~ N(μ = 21 ; σ = 7)

X ~ N(21, 7)

Probability that a trial lasted atleast 24 days :

P(X ≥ 24) :

The standardized score :

Z = (x - μ) / σ ; (24 - 21) / 7 ; 3 / 7 = 0.4286

Hence,

P(Z ≥ 0.4286) = 0.33411

The probability that a particular criminal trial lasted atleast 24 days is 0.33411