High School

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**Background:** Three students were asked to complete an assignment with the following tasks:

(a) Flip a coin 30 times and note the number of heads observed in the 30 flips.

(b) Repeat Step (a) 100 times to obtain 100 observations of the random variable \( x = \) number of heads in 30 flips.

(c) Construct a dotplot of the 100 \( x \) values.

**Questions:**

1. Do you think that any of the three students made up the \( x \) values shown in their dotplot? If so, which ones, and what about the dotplot makes you think the student did not actually do the coin flipping? Support your answer with a simulation in Python or a diagram in Python (show the code used).

2. Working as a group, each student in your class should flip a coin 30 times and note the number of heads in the 30 tosses. If there are fewer than 50 students in the class, each student should repeat this process until there are a total of at least 50 observations of \( x = \) number of heads in 30 flips. Using the data from the entire class, construct a dotplot of the \( x \) values. Support your answer with a simulation in Python or a diagram in Python (show the code used).

3. After looking at the dotplot in Step 2 that resulted from actually flipping a coin 30 times and observing the number of heads, reconsider your answers in Step 1. For each of the three students, explain why you now think that he or she did or did not actually do the coin flipping. Support your answer with a simulation in Python or a diagram in Python (show the code used).

Answer :

You can use Python libraries such as matplotlib or seaborn to create dot plots and simulate coin flips using random number generation functions.

1. To determine if any of the three students made up the x values shown in their dot plots, we can compare their dot plots to a simulation of randomly flipping a coin 30 times. By generating random numbers and counting the number of heads in each simulation, we can compare the distribution of the simulated data to the dot plots of the three students.

Here is an example of a Python simulation:

```python

import random

import matplotlib.pyplot as plt

# Simulating flipping a coin 30 times

def coin_flips():

flips = []

for _ in range(30):

flips.append(random.choice(['H', 'T']))

return flips.count('H')

# Simulating 100 observations

observations = []

for _ in range(100):

observations.append(coin_flips())

# Creating a dotplot of the simulated observations

plt.figure()

plt.plot(observations, [0.5]*len(observations), 'bo')

plt.xlabel('Number of Heads')

plt.ylabel('Frequency')

plt.title('Simulation Dotplot')

plt.show() ```

2. To construct a dotplot of the x values from the entire class, we can follow a similar approach as in the simulation above. Each student in the class should flip a coin 30 times and note the number of heads.

Here is an example of a Python simulation for the class:

``python

# Flipping a coin 30 times for each student in the class

class_observations = []

while len(class_observations) < 50:

class_observations.append(coin_flips())

3. After looking at the dotplot of the class observations, we can reconsider our answers for each of the three students. If their dotplots align with the class dotplot, it suggests that they actually performed the coin flipping

To know more about Python visit:

https://brainly.com/question/30391554

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