In Cary's basketball career, he's made 80% of his free throws, plus or minus 5%. If he attempts 200 free throws this season, what is the range of successful free throws he can expe... In Cary's basketball career, he's made 80% of his free throws, plus or minus 5%. If he attempts 200 free throws this season, what is the range of successful free throws he can expect to make? Show your calculation.
Understand the Problem
The question is asking for the calculation of the expected range of successful free throws based on a player's historical success rate and a given number of attempts. Specifically, Cary has made 80% of his free throws with a variability of 5%. We need to calculate the minimum and maximum expected successful free throws if he attempts 200 this season.
Answer
Cary can expect to make between 150 and 170 successful free throws.
Answer for screen readers
The range of successful free throws Cary can expect to make is from 150 to 170.
Steps to Solve
- Calculate the success rate and variability
Cary's success rate for free throws is 80%. The variability is given as 5%.
- Determine the effective success rate range
The minimum and maximum success rates can be calculated as follows:
- Minimum success rate: $80% - 5% = 75%$
- Maximum success rate: $80% + 5% = 85%$
- Calculate the expected successful free throws
To find the range of successful free throws based on 200 attempts, we calculate:
-
Minimum successful free throws: $$ \text{Minimum} = 200 \times 0.75 = 150 $$
-
Maximum successful free throws: $$ \text{Maximum} = 200 \times 0.85 = 170 $$
- State the range of successful free throws
The expected range of successful free throws is from the minimum to the maximum, which is from 150 to 170.
The range of successful free throws Cary can expect to make is from 150 to 170.
More Information
Cary's shooting percentage indicates a solid performance, and the variability suggests there may be fluctuations in his success due to various factors such as pressure, fatigue, or condition on the day of the game.
Tips
- Incorrectly using the variability percentage, such as not adjusting the base success rate correctly.
- Failing to multiply the success rates by the total number of attempts to find the expected successful throws.
AI-generated content may contain errors. Please verify critical information
