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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 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 21 days. c. If one of the trials is randomly chosen, find the probability that it lasted between 21 and 27 days.

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 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 21 days. c. If one of the trials is randomly chosen, find the probability that it lasted between 21 and 27 days.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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 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 21 days. c. If one of the trials is randomly chosen, find the probability that it lasted between 21 and 27 days.
Transcribed Image Text: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 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 21 days. c. If one of the trials is randomly chosen, find the probability that it lasted between 21 and 27 days.
Expert Solution
Step 1

(a)

The distribution of X is,

Here, X denote the number of days for randomly selected trial.

The distribution of X follows normal with mean µ and standard deviation σ.

Hence, the distribution of X follows normal with mean 22 and standard deviation 4.

Thus, the distribution of X is X~N(22, 4).

(b)

The probability that it lasted at least 21 days is 0.5987, which is obtained below:

PX≥x=1-PX≤x=1-Pz≤x-μσPX≥21=1-PX≤21=1-Pz≤21-224=1-Pz≤-0.25=1-0.40129   Use Standard Normal Table=0.5987

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