In-Class Project: Normal Distribution
Empirical/Theoretical Distributions & Discrete Data
Name _____________________
Class ___________________
The Masters golf tournament has been held since 1934 for every year (except 1943-1945
due to WWII). For the years 1934-2004, 3472 golfers have “made the cut” and completed
all 4 rounds of the tournament. The frequency distribution and histogram of first round
scores (among these golfers making the cut) is given below, with a superimposed normal
curve (=73.54, =3.08).
Score
More
Frequency
Proportion
63
1
0.00029
64
2
0.00058
65
6
0.00173
66
16
0.00461
67
46
0.01325
68
67
0.01930
69
151
0.04349
70
238
0.06855
71
337
0.09706
72
428
0.12327
73
467
0.13450
74
498
0.14343
75
397
0.11434
76
293
0.08439
77
203
0.05847
78
125
0.03600
79
78
0.02247
80
50
0.01440
81
28
0.00806
82
17
0.00490
83
7
0.00202
84
7
0.00202
85
4
0.00115
86
3
0.00086
87
1
0.00029
88
2
0.00058
0
0.00000
Histogram
600
500
400
Co
unt300
200
100
0
60
65
70
75
Round 1
80
1. Based on the Normal Distribution with =73.54 and =3.08, between what two
scores would we expect the middle 95% of scores to fall between?
85
90
2. What fraction of scores would we expect to be below 70?
3. What score would the lowest 5% of all scores be below?
4. For continuous distributions, the area below a single point is 0, but for discrete data
(like golf scores), the frequencies (proportions) are greater than 0. We can get around
this with a continuity correction. We can attribute (for instance) the area under the
normal curve between 69.5 and 70.5 to the score of 70. Thus, for part 2 above, we
could say what is the probability X<69.5 to represent the probability a golfer shot
below 70. How good does the normal model fit for given ranges of scores? Complete
the following table of theoretical (based on Z-table) and empirical (based on
frequency distribution above) probabilities. Note that par is 72 at Augusta National
Country Club.
Actual Range
Under 70
80 or above
Over par
Within 2 of par
CC Range
Z-Range
Theoretical
Empirical