(2) The Bright Electric Company produces large quantities of light bulbs per day. For the 75 watt light bulb that it is currently producing, it is going to be advertised to have mean life of 500 hours and variance of 256 hours. In order to verify this claim, a consumer protection group plans to take a sample of size n = 100 and observe the sample average X. If the manufacturer's claim is taken to be accurate what is the probability that the sample average will differ from 500 by more than 5 hours? When the actual sample was taken and the resulting sample average was observed, it was found to be 473 hours. Is the manufacturer's claim trustworthy? Solve this problem by taking the following four steps one by one. Step (i) Even though the population distribution is not going to be normal, the sample size is large enough so that the sampling distribution of X 100 is approximately normal. This is due to TTE CBS By luck CLT GCVF N/A (i- Select One) Step (ii) The problem wants us to compute P(|X 100 – 500| 2 5). which is the same as X 100 - 500 -5 5 1 — Р 16/10 16/10 16/10 Why: Lucky guess Standardization TTE GCVF CLT N/A (ii- Select One) Step (iii) The probability expression of the last part is approximately equal to 1 - P(-3.125

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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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.

(2) The Bright Electric Company produces large quantities of light bulbs per day. For the 75 watt light bulb that it is
currently producing, it is going to be advertised to have mean life of 500 hours and variance of 256 hours. In order to
verify this claim, a consumer protection group plans to take a sample of size n = 100 and observe the sample average
X. If the manufacturer's claim is taken to be accurate what is the probability that the sample average will differ from 500
by more than 5 hours? When the actual sample was taken and the resulting sample average was observed, it was found to
be 473 hours. Is the manufacturer's claim trustworthy:
Solve this problem by taking the following four steps one by one.
Step (i) Even though the population distribution is not going to be normal, the sample size is large enough so that the
sampling distribution of X 100 is approximately normal. This is due to
TTE
CBS
By luck
CLT
GCVF
N/A
(i- Select One)
Step (ii) The problem wants us to compute P(|X 100 –
500| 2 5). which is the same as
-5
Х 100 — 500
-
1 - P
16/10
16/10
16/10
Why:
Lucky guess
Standardization
TTE GCVF
CLT NIA
(ii- Select One)
Step (iii) The probability expression of the last part is approximately equal to
1 - P (-3.125 <Z < 3.125)
= 0.0018,
where Z ~ N(0, 1). Why:
Lucky guess
Standardization
TTE GCVF
CLT N/A
(iii- Select One)
Step (iv) An actual observed sample average turns out to be 473. In light of this information is the manufacturer's claim
trustworthy:
No
Yes
Maybe
Sometimes
Never
N/A
(iv- 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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