Yes, I can explain how to perform Z-score normalization using numpy and discuss the key differences between min-max normalization and Z-score normalization.

Z-score normalization, also known as standardization, is a common method used to normalize data by transforming it to have a mean of 0 and a standard deviation of 1. This allows the data to be compared on a common scale and helps to remove the effect of differences in scale or magnitude between variables.

Here is how to perform Z-score normalization using numpy:

```
import numpy as np

# create a sample dataset
data = np.array([10, 20, 30, 40, 50])

# calculate the mean and standard deviation
mean = np.mean(data)
std_dev = np.std(data)

# perform z-score normalization
z_score_norm = (data - mean) / std_dev

print(z_score_norm)
```
Output:
```
[-1.41421356 -0.70710678  0.          0.70710678  1.41421356]
```

As for the key differences between min-max normalization and Z-score normalization, they are as follows:

1. Min-max normalization scales the data to a fixed range, typically between 0 and 1, by subtracting the minimum value and dividing by the range of the data. This method is useful when you want to preserve the shape of the distribution but force the values into a specific range. Z-score normalization, on the other hand, standardizes the data by subtracting the mean and dividing by the standard deviation, which can cause the distribution to shift and become centered at 0 with a standard deviation of 1.

2. Min-max normalization is sensitive to outliers because it scales the data based on the minimum and maximum values, which can be skewed by extreme values. Z-score normalization, on the other hand, is less sensitive to outliers because it is based on the mean and standard deviation, which are less affected by extreme values.

3. Min-max normalization can be useful when dealing with non-normal distributions because it preserves the shape of the distribution. Z-score normalization is typically used with normal distributions or when you want to standardize the data for use in a machine learning algorithm that assumes normally distributed data.

In summary, min-max normalization and Z-score normalization are two common methods for normalizing data, and they have different effects on the data distribution. Min-max normalization is useful when you want to preserve the shape of the distribution and force the data into a specific range, while Z-score normalization is useful when you want to standardize the data and compare variables on a common scale.
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