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The phrase "a normal distribution thereby" is not correct and may be confusing in written English.
It could be used in a context where you are explaining the implications or results of a normal distribution, but the word "thereby" may not fit well without additional context.
Example: "The data follows a normal distribution thereby indicating that most values cluster around the mean."
Alternatives: "a normal distribution consequently" or "a normal distribution as a result".
Exact(1)
Log2-transformed ratio (AD/control) of protein abundances fit a normal distribution, thereby permitting determination of significantly changed protein abundances in the AD pool.
Similar(59)
To do so, we approximate the distribution at each position by a mixture of two normal distributions, thereby dividing them into two clusters.
These results suggest that protein 4.1B is required to maintain a normal distribution of Caspr and thereby an efficient barrier at the MN para-AIS: when disturbed, Kv1 channels invade the MN para-AIS.
Pathological examination of post-mortem tissue of FUS mutation carriers shows predominant degeneration of lower motor neurons with FUS-positive cytoplasmic inclusions and a normal distribution of TDP-43, thereby distinguishing them from other ALS cases [ 72, 80, 116, 196].
As T-scores are normally distributed by definition, the skewed distribution is thereby transformed into a normal distribution.
The method requires a normal distribution of the noise, which was confirmed by a χ-test, thereby allowing the use of the T distributions.
The total materials current linking machines i and j in period t created by all parts (i.e. f tij ) is obtained using Eq. (9) in which (f_{tijk}) is a random variable with normal distribution and thereby (f_{tij}) is also a random variable with a normal distribution having the expectation and variance shown in Eqs.
That is a normal distribution.
The mean is a parameter of a normal distribution.
Because log x as a normal distribution had mean mu.
And one of the most universal random variable, our distribution is a normal distribution.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com