) Construct a binomial distribution using n equals 8 and p equals 0.40. 

x

​P(x)

0
  
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1
  
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2
  
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3
  
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4
  
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5
  
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6
  
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7
  
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8
  
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round 4 decimal places

Here is the binomial distribution with \( n = 8 \) and \( p = 0.40 \), with probabilities rounded to four decimal places:

| \( x \) | \( P(x) \) |
|:---:|:-------:|
|  0  |  0.0168 |
|  1  |  0.0896 |
|  2  |  0.2090 |
|  3  |  0.2787 |
|  4  |  0.2322 |
|  5  |  0.1239 |
|  6  |  0.0413 |
|  7  |  0.0079 |
|  8  |  0.0007 |

Would you like further details on any of these calculations, or do you have any other questions?

Here are 5 related questions:
1. What is the significance of each value of \( x \) in the binomial distribution?
2. How does the value of \( n \) affect the shape of the binomial distribution?
3. Can you explain how to calculate the mean and variance of this binomial distribution?
4. How would the binomial distribution change if \( p \) were increased to 0.60?
5. What is the relationship between the binomial distribution and the normal distribution?

**Tip:** Understanding the symmetry or skewness of the binomial distribution can give insights into the likelihood of outcomes, especially for different values of \( p \).

Explore how to construct a binomial distribution with n=8 and p=0.40. This distribution showcases probabilities for different values of x, ranging from 0 to 8, rounded to four decimal places. Understand the significance of each probability value and its implications in statistical analysis. Suitable for advanced high school students.

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