91Ó°ÊÓ

A basketball player claims to make \(47 \%\) of her shots from the field. We want to simulate the player taking sets of 10 shots, assuming that her claim is true. To simulate the number of makes in 10 shot attempts, you would perform the simulation as follows: (a) Use 10 random one-digit numbers, where \(0-4\) are a make and \(5-9\) are a miss. (b) Use 10 random two-digit numbers, where \(00-46\) are a make and \(47-99\) are a miss. (c) Use 10 random two-digit numbers, where \(00-47\) are a make and \(48-99\) are a miss. (d) Use 47 random one-digit numbers, where 0 is a make and \(1-9\) are a miss. (e) Use 47 random two-digit numbers, where \(00-46\) are a make and \(47-99\) are a miss.

Step by step solution

01

Understand the Success Rate

The basketball player's claim states that she makes 47% of her shots from the field. This implies that in any set of attempts, 47% are expected to be successful shots.

02

Analyze Option (a)

In option (a), numbers 0-4 are considered makes. This setup implies a success rate of 5/10 = 50%. This is not aligned with the given success probability of 47%.

03

Analyze Option (b)

Option (b) states that numbers 00-46 are makes. This corresponds to 47 possible successful outcomes out of 100, matching the 47% success rate.

04

Analyze Option (c)

In option (c), numbers 00-47 are makes, which gives a success rate of 48 out of 100, or 48%, which is higher than the expected 47%.

05

Analyze Option (d)

Option (d) utilizes the numbers 0-9, and only 0 represents a make, indicating a 1/10 = 10% success rate, which is far lower than the desired 47%.

06

Analyze Option (e)

Option (e) talks about 47 random two-digit numbers with numbers 00-46 being makes. Given that we are out of 47 numbers, this scenario is illogical as there are only 10 two-digit numbers (00-09) represented, hence the setup is flawed.

07

Identify the Correct Simulation

Based on the options analyzed, option (b) correctly represents the 47% success rate with 47 valid success numbers (00-46) out of 100 possible two-digit numbers (00-99).

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Success Rate

When we talk about the success rate in a probability context, we're looking at the percentage of times a particular outcome occurs compared to all possible tries. Here, the basketball player's claim of making 47% of her shots means that, on average, she expects to successfully make 47 out of every 100 shots. This expected success is fundamental for setting up accurate simulations. By clearly defining successful outcomes in our simulation, we ensure that the experiment reflects real-world scenarios. To simulate the 47% success rate properly, we needed to allocate the right portion of outcomes to represent successes, making it critical to align the random numbers with the expected probability.

Random Number Generation

Random number generation involves producing a sequence of numbers that lack any pattern. It's an essential tool in probability simulations because it mimics the variability and unpredictability of real-world events. In our exercise, random numbers serve as trial results, determining whether a shot is a make or miss. By assigning specific numbers to successes and failures according to the desired success rate, we can simulate various outcomes across multiple trials. For precise simulations, such as determining a player's shot success, it's crucial to ensure randomness to avoid bias and accurately reflect probabilities like the 47% in our scenario.

Two-digit Probability Simulation

Two-digit probability simulations involve using numbers from 00 to 99 to replicate chances or likelihoods within the range of 0% to 100%. By using numbers 00 to 46 to signify a successful shot in our exercise, we capture the 47% success probability that the basketball player claims. This setup provides an intuitive and manageable framework for visualizing and running multiple trials. Each number from 00 to 99 has an equal chance of appearing when randomly generated, making the setup reliable for simulations. In this way, the two-digit approach ensures every new trial can be trusted to reflect the 47% success rate accurately, as the allocation perfectly matches the claimed shooting performance.