Tournament scores for 92 golfers are distributed normally. Two statistics from this tournament are given below.
Mean: 74
Standard deviation: 2.5
What is the approximate percentage of golfers that scored higher than 79?
79 is 2 sd above the mean ... z-score is 2
from the z-score table ... % of population above 2 ... 100% - 97.72%
To find the approximate percentage of golfers who scored higher than 79, we need to use the concept of standard deviation and the normal distribution.
Step 1: Calculate the z-score
The z-score measures the number of standard deviations a given data point is away from the mean. In this case, we want to find the z-score for 79.
z-score = (x - mean) / standard deviation
z-score = (79 - 74) / 2.5
z-score = 5 / 2.5
z-score = 2
Step 2: Find the area under the standard normal curve
To find the area under the standard normal curve corresponding to a z-score of 2, we can refer to a z-score table or use a statistical calculator. The table or calculator will give us the percentage of data points below a given z-score. Since we are interested in the percentage of golfers who scored higher than 79, we need to find the percentage of data points that fall to the right of the z-score of 2.
From the z-score table or calculator, we find that the percentage of data points below a z-score of 2 is approximately 97.72%.
Step 3: Calculate the percentage of golfers scoring higher than 79
To find the percentage of golfers who scored higher than 79, we subtract the percentage we found in step 2 from 100%.
Percentage of golfers scoring higher than 79 = 100% - 97.72% = 2.28%
Therefore, approximately 2.28% of the golfers scored higher than 79.