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Chapter 4: Problem 7

Describe the simulation procedure. (For example, to simulate 10 births, use a random number generator to generate 10 integers between 0 and 1 inclusive, and consider 0 to be a male and 1 to be a female.) Shaquille O'Neal Shaquille O'Neal was a professional basketball star who had a reputation for being a poor free-throw shooter. In his career, he made 5935 of 11,252 free throws that he attempted, for a success ratio of 0.527. Describe a procedure for using software or a TI- \(83 / 84\) Plus calculator to simulate his next free throw. The outcome should be an indication of one of two results: (1) The free throw is made; (2) the free throw is missed.

Short Answer

Expert verified
Generate a random number, and if it is 鈮� 0.527, the free throw is made; otherwise, it is missed.

Step by step solution

01

- Understand the Success Ratio

Identify Shaquille O'Neal's success ratio for free throws. His success ratio is given as 0.527 (or 52.7%).
02

- Set Up the Random Number Generator

To simulate the free throw, use a random number generator that produces a value between 0 and 1 inclusive.
03

- Define the Threshold

Set the threshold value to 0.527. If the generated random number is less than or equal to 0.527, the free throw is considered made. Otherwise, it is missed.
04

- Simulate the Free Throw

Generate a random number using the TI-83/84 Plus calculator鈥檚 random number feature (`rand`).
05

- Compare the Random Number

If the random number is 鈮� 0.527, record that the free throw is made. If it is > 0.527, record that the free throw is missed.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

random number generation
Random number generation is the process of producing numbers that lack any predictable pattern. This is essential in simulations to imitate real-world scenarios. In the context of simulating Shaquille O'Neal's free throw success, we need random numbers between 0 and 1. Each generated number will represent an outcome of his free throw: either made or missed. For example, a random number lower than or equal to 0.527 indicates a successful throw, while a number greater than 0.527 means a missed throw.
success ratio
The success ratio quantifies how often a specific outcome occurs. It's calculated as the number of successful attempts divided by the total number of attempts. For Shaquille O'Neal, his success ratio for free-throws is 0.527 (or 52.7%). This figure means that about 52.7% of his free throws were successful during his career. To use this ratio in a simulation, we compare it against randomly generated numbers to determine if a simulated free throw is made or missed.
threshold comparison
A threshold comparison involves checking if a generated number is below or above a certain value. For Shaquille O'Neal's free throw simulation, our threshold is set at 0.527. Here's how it works:
  • Generate a random number between 0 and 1.
  • Compare this number to the threshold of 0.527.
  • If the number is 鈮� 0.527, the throw is made.
  • If the number is > 0.527, the throw is missed.
By repeating this comparison multiple times, we can simulate multiple free throw attempts and mimic his actual performance.
TI-83/84 Plus calculator
The TI-83/84 Plus calculator is a powerful tool for running simulations. It includes a built-in random number generator function (`rand`). Here's how you can simulate a free throw on this calculator:
  • Turn on the calculator and press the `MATH` button.
  • Scroll to the `PRB` menu and select `rand` to generate a random number between 0 and 1.
  • Compare the generated number to 0.527 to determine if the free throw is made or missed.
By using this function repeatedly, you can simulate the outcome of multiple free throws efficiently.

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