In-Class Project: Normal Distribution



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 (μ=73.54, σ=3.08).

1. 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 between?

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 ................
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