Treat the number of months X after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - U( b. Suppose that 38 people are surveyed. What is the distribution of for this sample? I - N c. What is the probability that the average birth month of the 38 people will be less than 4.3?
Treat the number of months X after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - U( b. Suppose that 38 people are surveyed. What is the distribution of for this sample? I - N c. What is the probability that the average birth month of the 38 people will be less than 4.3?
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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![**Transcription for Educational Website:**
Treat the number of months \( X \) after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible.
a. What is the distribution of \( X \)? \( X \sim U(\boxed{0}, \boxed{12}) \)
b. Suppose that 38 people are surveyed. What is the distribution of \( \bar{x} \) for this sample?
\[
\bar{x} \sim N\left(\boxed{6}, \boxed{\frac{\sqrt{12}}{\sqrt{38}}}\right)
\]
c. What is the probability that the average birth month of the 38 people will be less than 4.3?
\[
\boxed{0.0259}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4cbdcd8-71de-429b-b001-27d54b327ca5%2F5a3dd3e4-dd4c-44b5-b993-2259ceb7fcfe%2Ft7hnyxn_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
Treat the number of months \( X \) after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible.
a. What is the distribution of \( X \)? \( X \sim U(\boxed{0}, \boxed{12}) \)
b. Suppose that 38 people are surveyed. What is the distribution of \( \bar{x} \) for this sample?
\[
\bar{x} \sim N\left(\boxed{6}, \boxed{\frac{\sqrt{12}}{\sqrt{38}}}\right)
\]
c. What is the probability that the average birth month of the 38 people will be less than 4.3?
\[
\boxed{0.0259}
\]
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