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 4 days. Let X be the number of days for a randomly selected trial. Round all answers to 3 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 19 days. _____

c. If one of the trials is randomly chosen, find the probability that it lasted between 25 and 31 days. _____

d. 86% of all of these types of trials are completed within how many days? _____ (Please enter a whole number)  

Answer 1

Solution :

(a)

X ~ N(22 , 4)

(b)

P(x 19) = 1 - P(x   19)

= 1 - P[(x - ) / (19 - 22) / 4]

= 1 -  P(z 0.75)  

= 0.7734

(c)

P(25 < x < 31) = P[(25 - 22)/ 4) < (x - ) /  < (31 - 22) / 4) ]

= P(0.75 < z < 2.25)

= P(z < 2.25) - P(z < 0.75)

= 0.9878 - 0.7734

= 0.2144

(d)

P(Z < 1.08) = 0.86

Using z-score formula,

x = z * +

x = 1.08 * 4 + 22 = 26.32 = 26