Answered: The average amount of money spent for…

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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Question

The average amount of money spent for lunch per person in the college cafeteria is $7.41 and the standard deviation is $2.2. Suppose that 16 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.

What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $7.515 and $8.22.

Expert Solution

Step 1:

$\mathbf{Solution }$

$\\\mathbf{given:}\;mean\;(\mu)=7.41,\;standard\;deviation\;(\sigma)=2.2,\;sample\;size\;(n)=16$

$\mathbf{{\color{Blue} \mathbf{a.}}\;X\sim N(\mu,\;\sigma)\Rightarrow X\sim N({\color{Red} 7.41},\;{\color{Red} 2.2})}$

$\mathbf{{\color{Blue} \mathbf{b.}}\;\bar x\sim N\left ( \mu,\;\frac{\sigma}{\sqrt{n}} \right )\Rightarrow X\sim N({\color{Red} 7.41},\;{\color{Red} 0.55})}$

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