In case you're wondering what the abbreviations stand for:CLT: central limit theoremTTE: Time to the event (i don't think we took this in class though, could be there for no reason)GCVF: Generalized change of variable formula CBS: Cauchy bunyakowski schwarz. If there is an abbreviation you don't understand, please ignore it because it might not mean anything. (1) We select n = 50 real numbers at random and then round them off to the nearest integers, before adding them all up.Find an approximation to the probability that the difference between the sum of the rounded numbers and the sum of theoriginal numbers is no more than 3. Solve this problem by taking the following three steps one by one.Step (i) Let Let Z1 , Z2,for instance 13.49 and will be rounded to 13 and 13.51 will be rounded to 14. You may round up or down the number13.50, which carries zero probability anyway. Why is it reasonable to assume that the rounding error, Zn be the original numbers and let N1, N2, ·.. , Nn be their rounded off version. That is,iidU; = Z; - N; Uniform(-,), i = 1,2, .., n?The correct answer isCLTTTECBSGCVFNone of the aboveN/A(i- Select One)Step (ii) We want to compute the probability P (| E Z¡ – E1 Ni| < 3), which is equal to(ωP ( ΣU < 3 ) .() P ( Σ UI 3).(c) P (E, U; < 3).(d) P (E, Ui 2 3).i=1=1i=1(e) None of the aboveThe correct answer is(a)(b)(c)(d)(e)N/A(ii- Select One)Step (iii) The desired probability of Step (ii) is approximately equal to P(|N(0, 1)| < 3/12/50) = 0.86 due toTTVCBSGCVFCLTNone of the aboveN/A(iii- Select One)

Given: Sample size (n) = 50 Zi = original number Ni = rounded off number Ui=Zi-Ni ~U-12,12…

Answered: n case you're wondering what the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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In case you're wondering what the abbreviations stand for:

CLT: central limit theorem

TTE: Time to the event (i don't think we took this in class though, could be there for no reason)

GCVF: Generalized change of variable formula

CBS: Cauchy bunyakowski schwarz.

If there is an abbreviation you don't understand, please ignore it because it might not mean anything.

(1) We select n = 50 real numbers at random and then round them off to the nearest integers, before adding them all up.
Find an approximation to the probability that the difference between the sum of the rounded numbers and the sum of the
original numbers is no more than 3. Solve this problem by taking the following three steps one by one.
Step (i) Let Let Z1 , Z2,
for instance 13.49 and will be rounded to 13 and 13.51 will be rounded to 14. You may round up or down the number
13.50, which carries zero probability anyway. Why is it reasonable to assume that the rounding error
, Zn be the original numbers and let N1, N2, ·.. , Nn be their rounded off version. That is,
iid
U; = Z; - N; Uniform(-,), i = 1,2, ..
, n?
The correct answer is
CLT
TTE
CBS
GCVF
None of the above
N/A
(i- Select One)
Step (ii) We want to compute the probability P (| E Z¡ – E1 Ni| < 3), which is equal to
(ωP ( ΣU < 3 ) .
() P ( Σ UI 3).
(c) P (E, U; < 3).
(d) P (E, Ui 2 3).
i=1
=1
i=1
(e) None of the above
The correct answer is
(a)
(b)
(c)
(d)
(e)
N/A
(ii- Select One)
Step (iii) The desired probability of Step (ii) is approximately equal to P(|N(0, 1)| < 3/12/50) = 0.86 due to
TTV
CBS
GCVF
CLT
None of the above
N/A
(iii- Select One)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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