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Guidelines to problems
chapter 7 (ST210)
Nutan S. Mishra
Department of Mathematics and Statistics
University of South Alabama
Exercise 7.28
It is given that population distribution is left
skewed, that is it has elongated tail on the
left hand side.
If we draw a sample of size n=400 from such
a population and compute the sample mean x
then what will be distribution of x ?
Since the sample size is large, by application of Central Limit Theorem,
distribution of x is approximately normal
x ~ N ( ,  / 400)
Exercise 7.32
X= amount of time taken to deliver the
lunch order.
X~N( 6.7, 2.1)
That is on the average
they take 6.7
x
minutes to deliver the lunch order with
a standard deviation of 2.1 minutes.
If we draw the samples of size 16 and compute
distribution of x ?
then what will be the
Though the sample is small ( n=16), since the parent distribution is normal
the distribution of x will be normal
x
~ N( 6.7, 2.1/√16)
Exercise 7.36
Its given in problem that
X= weight of a person in a small town
Average weight of all the persons in the town
is µ = 133 lb , with a standard deviation of 24lb
Also given that population is right skewed.
If we draw samples of size 45 from this population, what would be the distribution
of the sample mean?
Though parent population is skewed, since we are drawing large samples (n=45),
by application of central limit theorem, the distribution of sample mean is normal
x ~N( 133, 24/√45)