Can any data be transformed into a standard normal distribution?

There is a standardized transformation which can transform a normal distribution to standard normal distribution:

I am wondering given a uniform distribution or any other distribution, can we transform it into a standard normal distribution using the above equation?

It is difficult to see from the following codes.

import numpy as np
import matplotlib.pyplot as plt

x = np.random.randint(0, 10000, (1, 100))
y = np.random.randint(0, 4000, (1, 100))

z = np.random.randn(1, 100)

x_s = (x - x.mean()) / x.std()
y_s = (y - y.mean()) / y.std()

# plt.hist(x_s, bins=1)

import seaborn as sns

# sns.distplot(x, rug=True, bins=None)
sns.distplot(x_s, rug=True, bins=None)
# sns.distplot(z, rug=True, bins=None)

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