Question

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 17 days and a standard deviation of 6 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. If one of the trials is randomly chosen, find the probability that it lasted at least 13 days.

c. If one of the trials is randomly chosen, find the probability that it lasted between 18 and 24 days.

d. 87% of all of these types of trials are completed within how many days? (Please enter a whole number)

Answer 1

Solution :

Given that ,

a.

X N (17 , 6)

b.

P(x 13) = 1 - P(x   13)

= 1 - P[(x - ) / (13 - 17) / 6]

= 1 -  P(z -0.67)   

= 1 - 0.2514

= 0.7486

Probability = 0.7486

c.

P(18 < x < 24) = P[(18 - 17)/ 6) < (x - ) /  < (24 - 17) / 6) ]

= P(0.17 < z < 1.17)

= P(z < 1.17) - P(z < 0.17)

= 0.879 - 0.5675

= 0.3115

Probability = 0.3115

d.

Using standard normal table ,

P(Z < z) = 87%

P(Z < 1.13) = 0.87

z = 1.13

Using z-score formula,

x = z * +

x = 1.13 * 6 + 17 = 24

24 day