Tournament scores for 92 golfers are distributed normally. Two statistics from this tournament are given below.
Mean score: 74
Standard Deviation: 2.5
(Refer to the given golf tournament statistics.)
What is the approximate percentage of golfers that scored between 69 and 79?
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To find the approximate percentage of golfers that scored between 69 and 79, we can use the concept of the empirical rule for normal distributions.
According to the empirical rule, for a normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
In this case, the mean score is 74, and the standard deviation is 2.5.
To find the percentage of golfers that scored between 69 and 79, we need to calculate how many standard deviations away these scores are from the mean.
First, we calculate the z-scores for the two scores:
For a score of 69:
z-score = (69 - 74) / 2.5 = -2
For a score of 79:
z-score = (79 - 74) / 2.5 = 2
Now, we can use a standard normal distribution table or calculator to find the percentage of data within these z-scores.
From the table or calculator, we find that the area under the curve between -2 and 2 is approximately 0.9545.
To convert this to a percentage, we multiply 0.9545 by 100: 0.9545 * 100 = 95.45%.
Therefore, approximately 95.45% of the golfers scored between 69 and 79 in this tournament.