In-Class Project: Normal Distribution Name ____________________________________ Date __________ Period _________ The Masters Golf Tournament has been held since 1934 for every year (except 1943-1945 due to WWII) and is played in Augusta, GA. 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 (from the golfers making the cut) is given below, with a superimposed normal curve (µ=73.54, σ=3.08).

1. If par for this course is 72, how would you describe the scores in the histogram in relation to par?

What does this tell you about the skill level of the players?

2. Assuming a Normal distribution, what percent of scores would we expect to be below 70?

Score 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

More 0 0.00000

0

100

200

300

400

500

600

Count

60 65 70 75 80 85 90Round 1

Histogram

3. Based on the Normal Distribution with µ=73.54 and σ=3.08, between what two scores would we

expect the middle 95% of scores to fall? (Hint: use the normal curve below to help you.)

4. Assuming a Normal distribution with µ=73.54 and σ=3.08, what score would the lowest 5% of all

scores be below?

PROJECT: NORMAL PROBABILITY DISTRIBUTION

Objective: Use the Normal Probability Distribution to make decisions about a

population.

Scenario: An apparel company makes blue jeans and leather pants.

I. The female division.

Female Height in inches

66.4 68.1 66.7 67.9 63.1 67.8 66.1 68.9 66.1 69.2 64.9 67.6 57.6 65.1 66.7 67.8 66.8 63.6 67.5 60.2 69.4 68.4 62.2 67.2 64.7 66.3 64.2 62.2 64.3 67.2 63.2 58.1

A. Use the "Statistics" function of your calculator to find the sample mean and sample

standard deviation for the data. (Round to tenths.)

1. Mean ____________ 2. Standard deviation __________

Use these statistics when calculating the standard (z) scores.

B. Use the Normal Probability Distribution table to find:

1. What percent of female adults are taller than 6 feet (72 inches)? __________

2. What percent of female adults are taller than 5 feet (60 inches)? __________

3. What percent of female adult heights are between 60 inches

and 72 inches? __________

C. Because of the high cost of leather, the company has decided they cannot profitably make

leather pants in all sizes.

Use the Normal Probability Distribution table to find the heights corresponding to the

following percentages. These are the heights of the shortest and tallest females who

cannot purchase leather pants from this company. (Round to tenths.)

1. The bottom 8%

2. The upper 6%

II. The male division

Male Height in inches

68 65.5 68.1 72.5 65.4 71.2 67.7 73.5 67.7 65.1 65.3 65.5 72 73.2 62.5 77.2 70.5 66.7 67.5 70.2 67.4 71.8 65.1 67.2 66.3 69.3 67.7 67 73.8 66.5 66.1 68.6

A. Use the "Statistics" function of your calculator to find the sample mean and sample

standard deviation for the data. (Round to tenths.)

1. Mean __________ 2. Standard deviation __________

Use these statistics when calculating the standard (z) scores.

B. Use the Normal Probability Distribution table to find:

1. What percent of male adults are shorter than 6 feet (72 inches)? __________

2. What percent of male adults are shorter than 5 feet (60 inches)? __________

3. What percent of male adult heights are between 60 inches and 72 inches? __________

D. Because of the high cost of leather, the company has decided they cannot profitably make

leather pants in all sizes.

Use the Normal Probability Distribution table to find the heights corresponding to

the following percentages. These are the heights of the shortest and tallest males who

cannot purchase leather pants from this company. (Round to tenths.)

1. The bottom 9% __________

2. The upper 7% __________