ENME392 Spring 2012
Homework 7 Solutions
Total number of points: 100
The questions are a followup to lastweek’s assignment: (80 pts)
a)
Group your numberofheads data into 25 groups of 4 points by taking the results of the
first 4 tosses, then the next 4, and so on.
Calculate the average and the variance of the
number of heads in these groups.
Show the results of your calculations in a table.
b)
Make a histogram showing the frequency distribution of the average number of heads.
Show your binned data.
c)
On the same plot, show the expected sampling frequency distribution.
Show the results
of your calculations in a table.
d)
On the same plot, show the binomial frequency distribution calculated in part (b) of last
week’s homework assignment.
The experimental data are expected to follow the sampling distribution
X
Z
/
n
μ
σ

=
.
The values
to use here are m = 20, p = q = 0.5,
μ
= mp = 10,
σ
= sqrt(mpq) = 2.236, n = 4.
The calculation
in the z column was
(L55  $O$49)/($O$50/SQRT($O$53))
where L55 contained the value in the X column, $O$49 the mean, $O$50 the standard deviation,
and $O$53 the value for n.
The sampling probability was found using
NORMDIST(M55,0,1,FALSE)
where M55 contained the Z values.
The sampling frequency was found by multiplying by 25.
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Experimental
Sampling
Dist. of Mean
Bin
Frequency
X
Z
Sampling
Probability
Expected
Sampling
Frequency
5.5
0
0
8.944
0.000
0.00
11.00
6.5
1
1
8.050
0.000
0.00
11.50
7.5
0
2
7.155
0.000
0.00
9.75
8.5
1
3
6.261
0.000
0.00
9.25
9.5
8
4
5.367
0.000
0.00
11.00
10.5
7
5
4.472
0.000
0.00
9.75
11.5
7
6
3.578
0.001
0.02
10.50
12.5
1
7
2.683
0.011
0.27
9.50
More
0
8
1.789
0.081
2.01
9.25
9
0.894
0.267
6.69
9.25
25
10
0.000
0.399
9.97
8.25
11
0.894
0.267
6.69
10.00
12
1.789
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 Spring '10
 Cukier
 Normal Distribution, Standard Deviation, Variance, Frequency distribution

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