ME 365
Homework Set 5
Out September 22 , 2011
Due September 29, 2011
Problem No. 1
Each member of a class of 50 students is given a piece of the same metal (or what is
said to be the same metal) and told to find its density.
From the 50 results the mean
and the standard deviation
are calculated.
Given the following tabulation of
the observed number of values within each internal,
Bin k
Values of
in bin k
Observations
O
k
in bin k
1
Below
12
2
Between
and
13
3
Between
and
11
4
Above
14
(a) Determine
2
assuming a Gaussian distribution.
Solution:
Using table A of the appendix to chapter 4:
The area under the normal distribution curve for the interval
to
is
68.27%.
From this the probability for each interval can be determined:
Bin 1 & Bin 4:
P
1
P
4
1
0.6827
2
0.15865
Bin 2 & Bin 3:
P
2
P
3
0.6827
2
0.34135
Multiplying each probability by the total number of measurements, 50, the expected
number of values in each bin is determined and the following table can be
constructed.
Bin k
Values of
in bin
Observations
O
k
Expected
E
k
O
k
E
k
2
E
k
1
Below
12
7.9325
2.085667
2
Between
and
13
17.0675
0.969360
3
Between
and
11
17.0675
2.156998
4
Above
14
7.9325
4.640978
2
9.853003
(b) State your reasons for either accepting or rejecting the Gaussian hypothesis.
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 Fall '07
 MERKLE
 Normal Distribution, AE, bin k

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