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# RES 341 Week 5 Individual Assignment Exercises From the E-Text.

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Chapter Review questions
RES 341

5) State the main points of the Central Limit Theorem for a mean.
The Central Limit Theorem (CLT) states that the sample mean . x is centered at μ and
follows a normal distribution if n is large, regardless of the population shape.
6) Why is population shape of concern when estimating a mean? What does sample size
have to do with it?
The population shape is figured out by using an arithmetic mean in which is not an a precise
measurement. The population shape often produces the frequency of value that can be acquired
by sampling the whole population. When samples are done in a small “fashion” then one is not
able to determine if the sample represents the mass. As to when the sample size increases it is
easier to determine if the sample represents the mass correctly.

Chapter Exercises
8.46
A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed
ona very accurate scale. The results in grams were:
3.087, 3.131, 3.241, 3.241, 3.270, 3.353, 3.400, 3.411, 3.437, 3.477
(a) Construct a 90 percent confidence interval for the true mean weight.
Equation = z*sigma/square root(n)
1.6455*0.13199/( square root of 10) = 0.06868136
(b) What sample size would be necessary to estimate the true weight with an error of ± 0.03
grams with 90 percent confidence?
x-bar = 3.3048
(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during
manufacture. (Data are from a project by MBA student Henry Scussel.)
90% CI = (3.3048-0.06866, 3.3048+0.06866)