STA 201 CASE study Chest size
Chapter 6 Case Study: Chest size of Scottish Militiamen p. 295
a.
Chest size (in)
Frequency
Relative Frequency
33
3
0.000523
34
19
0.003315
35
81
0.014131
36
189
0.032973
37
409
0.071354
38
753
0.131368
39
1062
0.185276
40
1082
0.188765
41
935
0.163119
42
646
0.112701
43
313
0.054606
44
168
0.029309
45
50
0.008723
46
18
0.003140
47
3
0.000523
48
1
0.000174
5732
1
b.
(μ=39.85, σ=2.07)
The normal curve is the one whose parameters are the same as the mean and standard deviation variable, which are 39.85 and 2.07, respectively. Thus the required normal curve has parameters μ=39.85 and σ=2.07.
c.
Chest size (in)
Frequency
Relative Frequency
33
3
0.000523
34
19
0.003315
35
81
0.014131
36
189
0.032973
37
409
0.071354
38
753
0.131368
39
1062
0.185276
40
1082
0.188765
41
935
0.163119
42
646
0.112701
43
313
0.054606
44
168
0.029309
45
50
0.008723
46
18
0.003140
47
3
0.000523
48
1
0.000174
5732
1
Utilizing the green highlighted section above, the following was calculated:
189+409+753+1062+1082+935 equals 4430.
4430 is divided by 5732 to equal 0.7728. The percentage of militiamen in the survey with chest circumference between 36 and 41 inches is 77.28%.
d. z =
z =
= -2.10
z =
= 0.80
Table II was used to find the area under the standard normal curve.
The area to the left of -2.10 is 0.0179. The area to the left of 0.80 is 0.7881.
The area under the standard normal curve that lies between -2.10 and 0.79 is 0.7881 - 0.0179 = 0.7702.
An approximation to the percentage of militiamen in the survey with chest circumference between 35.5 and 41.5 inches is 77.02%.
In comparing the percentage of 77.02%militiamen in the survey to 77.28% found in part c, both percentages are close and both can round to 77%.
a.
Chest size (in)
Frequency
Relative Frequency
33
3
0.000523
34
19
0.003315
35
81
0.014131
36
189
0.032973
37
409
0.071354
38
753
0.131368
39
1062
0.185276
40
1082
0.188765
41
935
0.163119
42
646
0.112701
43
313
0.054606
44
168
0.029309
45
50
0.008723
46
18
0.003140
47
3
0.000523
48
1
0.000174
5732
1
b.
(μ=39.85, σ=2.07)
The normal curve is the one whose parameters are the same as the mean and standard deviation variable, which are 39.85 and 2.07, respectively. Thus the required normal curve has parameters μ=39.85 and σ=2.07.
c.
Chest size (in)
Frequency
Relative Frequency
33
3
0.000523
34
19
0.003315
35
81
0.014131
36
189
0.032973
37
409
0.071354
38
753
0.131368
39
1062
0.185276
40
1082
0.188765
41
935
0.163119
42
646
0.112701
43
313
0.054606
44
168
0.029309
45
50
0.008723
46
18
0.003140
47
3
0.000523
48
1
0.000174
5732
1
Utilizing the green highlighted section above, the following was calculated:
189+409+753+1062+1082+935 equals 4430.
4430 is divided by 5732 to equal 0.7728. The percentage of militiamen in the survey with chest circumference between 36 and 41 inches is 77.28%.
d. z =
z =
= -2.10
z =
= 0.80
Table II was used to find the area under the standard normal curve.
The area to the left of -2.10 is 0.0179. The area to the left of 0.80 is 0.7881.
The area under the standard normal curve that lies between -2.10 and 0.79 is 0.7881 - 0.0179 = 0.7702.
An approximation to the percentage of militiamen in the survey with chest circumference between 35.5 and 41.5 inches is 77.02%.
In comparing the percentage of 77.02%militiamen in the survey to 77.28% found in part c, both percentages are close and both can round to 77%.