The speeds of Novak Djokovic first serve are modeled by normal distribution. 5.48% of his first serves
Question:
The speeds of Novak Djokovic first serve are modeled by normal distribution. 5.48% of his first serves are greater than 120 mph 0.82% of his first serves are less than 100 mph 33.64% of his first serves are between 100 mph and 110 mph The given parameters are: --- mean ---- standard deviation (a) How often he serves faster than 120 mph This means that: Start by calculating the z-score So, the proportion of times is calculated using: Using z-score table, we have: Express as percentage Approximate (b) Proportion of times he serves lesser than 100 mph This means that: Start by calculating the z-score So, the proportion of times is calculated using: Using z-score table, we have: Express as percentage Approximate (c) Proportion of times he serves between 100 mph and 110 mph This means that: In (b) , when When x = 110, we have: So, the proportion of times is calculated using: This gives: Using z-score table, we have: Express as percentage Approximate Hence, 33.64% of his first serves are between 100 mph and 110 mph.
