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Material Type: Assignment; Professor: Aronne; Class: ELEMENTS OF STATISTICS; Subject: Mathematics; University: Montgomery College; Term: Unknown 1989;
Typology: Assignments
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HEAD CIRCUMFERENCE
Chapter 7 – Distribution of Sample Mean
old boys are normally distributed and have a mean of 41.1 cm and a standard deviation of 1.5 cm.
a) Give the shape, mean and standard deviation of the distribution of sample means for samples of
size 50.
Notice: the population is all two-month-old baby boys
The variable X is their head circumference in inches
X is Normal with 41.1 and 1.
According to the Central Limit Theorem, the distribution of sample means is normal for any
sample size because X is normally distributed. Hence, for samples of size 50, the distribution
of x
is also normal with
x
x
n
b) What is the probability that a sample of fifty 2-month-old babies have a head circumference of
at most 40.048 cm?
P x P z P z
9
With calculator: normalcdf(-10 ,40.048,41.1, ) =0.000004=
A head circumference of 40.048 cm is a very unusual result if the population mean is 41.1. It
is a more common result in a population with mean lower than 41.1 – then, we can
conclude .... see ***** in part (d)
c) If the population has a mean of 41.1 cm, the probability that a sample of size fifty has a mean of
40.048 or less is ___ 0.0000004 __________
This means that for samples of size 50, about ____ 4 _ samples in 10 million will result in a sample
mean of 40.048 or less when the population mean is 41.
Because this event only happens___ 4 ___ out of __ 10 million ___ times, we consider it to be usual/
unusual.
d) What may this result suggest?
**********This VERY UNUSUAL result suggests that probably this sample has been selected**
from a population with mean lower than 41.1.
In reality the sample of size 50 with a mean of 40.048 is the FHED sample that we have in
our calculator (2-month-old baby girls data). This result suggests that the mean head
circumference of 2-month-old baby girls is smaller than for boys.
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