Question

6 0082 Normal Distribution (Time to trial) notes and pages 252-256 A sociologist has been studying the criminal justice system in a large metropolitan city. She has found that during a 5 year study that the mean time between a person being arrested and their trial is normally dis ributed with a mean of 170 days and a standard deviation of 18 days. a. Based on the above information, what is the probability that a randomly selected person will go to trial less than 136 days after they are arrested? Show the graph of the standard normal distribution. Use 4 decimal places for final answer. This problem does not use correction for continuity. 3 points +2 points for standard normal graph pages 252-254 b. Based on the above information, what is the probability that a randomly selected person will have to wait between 183 and 237 days before they go to trial? Show the graph of the standard normal distribution. Use 4 decimal places for final answer. 3 points+ 2 points for standard normal graph C. What is the probability that a randomly selected person will have to wait more than 207 days before they go to trial? Show the graph of the standard normal distribution. Use 4 decimal places for final answer. 3 points+ 2 points for standard normal graph 25

Answer 1

Random variable X: Mean time between person being arrested and their trial.

X is normally distributed with mean =
u=170
and standard deviation =
0 = 18

a) Here we have to find P(X < 136)

P(X < 136) = PA- 136 –

                                        where z is standard normal variable

136 – 170 = P(z<-

                           = P(z < -1.89)                          (Round to 2 decimal)

                          = 0.0294                                 (From statistical table of negative z values)

Probability that the randomly selected person will go to trial less than 136 days after they are arrested is 0.0294

b) Here we have to find P(183<X<237)

183 – μ -μ Χ P(183 <X < 237) = P(-9 237 –μ.

                                        

183-170 2 37-170、 18

                                        = P(0.72 < z < 3.72)                (Round to 2 decimal)

                                        = P(z < 3.72) - P(z < 0.72)

                                        = 1 - 0.7642            (From statistical table of z values)

                                        = 0.2358

Probability that a randomly selected person will have to wait between 183 and 237days before they go to trial is 0.2358

c) Here we have to find P(X>207)

P(x > 207) = P(X-H 207 – H

                           

207 – 170 = P(2>

                           = P(z > 2.06)                        (Round to 2 decimal)

                           = 1 - P(z < 2.06)

                           = 1 - 0.9803                  (From statistical table of z values)

                            = 0.0197

Probability that a randomly selected person will have to wait more than 207 days before they go to trial is 0.0197

Graphs of standard normal variable z:

We have to find area of shaded region.

2.6 0.72 -189 2-0 2=0 2,06