I need the answer for Part 2 of a, b and c. Thank you ### Duration of Criminal Trials - Normal DistributionSuppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 20 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.#### Question Part (a)**Question:** What is the distribution of $ X $?**Answer:**$ X \sim N \left( \mu = 20, \sigma = 6 \right) $This means that $ X $ follows a normal distribution with a mean ($ \mu $) of 20 days and a standard deviation ($ \sigma $) of 6 days.#### Question Part (b)**Question:** If one of the trials is randomly chosen, find the probability that it lasted at least 16 days.**Answer:** Calculate the probability $ P(X \geq 16) $.Given in the answer box: 0.3334 (Answer is marked incorrect)#### Question Part (c)**Question:** If one of the trials is randomly chosen, find the probability that it lasted between 21 and 27 days.**Answer:** Calculate the probability $ P(21 \leq X \leq 27) $.Given in the answer box: 0.2595 (Answer is marked incorrect)### Tools for Assistance- **Question Help:** Written Example- **Message Instruction:** Message instructor for further assistance.### Actions- **Submit Question:** Button available to submit the question.- **Jump to Answer:** Button available to jump to the answer.This problem involves the application of properties of the normal distribution, specifically finding probabilities associated with a given normal distribution using the z-score formula and standard normal distribution tables or software.

a. The distribution of X is N(20, 36). That is, the distribution of a particular type of criminal…

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 20 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.

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 20 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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I need the answer for Part 2 of a, b and c. Thank you

### Duration of Criminal Trials - Normal Distribution

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 20 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.

#### Question Part (a)
**Question:**
What is the distribution of $ X $?

**Answer:**
$ X \sim N \left( \mu = 20, \sigma = 6 \right) $

This means that $ X $ follows a normal distribution with a mean ($ \mu $) of 20 days and a standard deviation ($ \sigma $) of 6 days.

#### Question Part (b)
**Question:**
If one of the trials is randomly chosen, find the probability that it lasted at least 16 days.

**Answer:**
Calculate the probability $ P(X \geq 16) $.

Given in the answer box: 0.3334 (Answer is marked incorrect)

#### Question Part (c)
**Question:**
If one of the trials is randomly chosen, find the probability that it lasted between 21 and 27 days.

**Answer:**
Calculate the probability $ P(21 \leq X \leq 27) $.

Given in the answer box: 0.2595 (Answer is marked incorrect)

### Tools for Assistance
- **Question Help:** Written Example
- **Message Instruction:** Message instructor for further assistance.

### Actions
- **Submit Question:** Button available to submit the question.
- **Jump to Answer:** Button available to jump to the answer.

This problem involves the application of properties of the normal distribution, specifically finding probabilities associated with a given normal distribution using the z-score formula and standard normal distribution tables or software.

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