Let RE = "rol| 10 dice" and A ="average number of dots on the 10 up-faces." The CLT tells us that A [: RE] has an approximate Normal distribution with mean 3.5 and standard deviation 0.54.
Let RE = "rol| 10 dice" and A ="average number of dots on the 10 up-faces." The CLT tells us that A [: RE] has an approximate Normal distribution with mean 3.5 and standard deviation 0.54.
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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![**Exercise 4.** Let \( RE = \) "roll 10 dice" and \( A = \) "average number of dots on the 10 up-faces." The CLT tells us that \( A \, \big[ :RE \big] \) has an approximate Normal distribution with mean 3.5 and standard deviation 0.54.
(a) Give an empirical interpretation of the process mean \( E(A) = 3.5 \), and of the process standard deviation \( sd(A) = 0.54 \). Hint: "If \( RE \) ['roll 10 dice'] were independently repeated a trillion times and the \( A \) value recorded each time, then the sample average of these trillion \( A \) values would be ... and the sample standard deviation of..."
(b) What is the probability of rolling the 10 dice and seeing an average below 3?
(c) Would you be surprised to roll the 10 dice and see a total number of dots of 50 or above? Explain your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7f33394-5a52-4a6c-8272-5682354fd51c%2F93dc412b-bbbd-4c94-b048-31174d824de9%2Fk5kfu1_processed.png&w=3840&q=75)
Transcribed Image Text:**Exercise 4.** Let \( RE = \) "roll 10 dice" and \( A = \) "average number of dots on the 10 up-faces." The CLT tells us that \( A \, \big[ :RE \big] \) has an approximate Normal distribution with mean 3.5 and standard deviation 0.54.
(a) Give an empirical interpretation of the process mean \( E(A) = 3.5 \), and of the process standard deviation \( sd(A) = 0.54 \). Hint: "If \( RE \) ['roll 10 dice'] were independently repeated a trillion times and the \( A \) value recorded each time, then the sample average of these trillion \( A \) values would be ... and the sample standard deviation of..."
(b) What is the probability of rolling the 10 dice and seeing an average below 3?
(c) Would you be surprised to roll the 10 dice and see a total number of dots of 50 or above? Explain your answer.
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