Mathematics: Which normal distribution has a wider spread: the one with mean 3 and standard deviation 4 or the one with mean 4 and standard deviation 3 ? the normal distribution with mean 4 and standard deviation 3 has the wider spread?

Which normal distribution has a wider spread: the

Ответ:

Apple557

11.03.2022

Mathematics

The correct option is 1. The normal distribution with mean 3 and standard deviation 4 has a wider spread.

Step-by-step explanation:

Normal distribution is defined by two variables, mean and standard deviation.

$Z=\frac{X-\mu}{\sigma}$

The spread of a normal distribution is not dependent on mean, it is completely dependent of standard deviation. Larger standard deviation means wider spread.

It is given that first normal distribution has

$\mu_1=3$

$\sigma_1=4$

Second normal distribution has

$\mu_2=4$

$\sigma_2=3$

Since $\sigma_1\sigma_2$ , therefore the normal distribution with mean 3 and standard deviation 4 has a wider spread.

Hence the correct option is 1.

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Which normal distribution has a wider spread: the one with mean 3 and standard deviation 4 or the one with mean 4 and standard deviation 3 ? the normal distribution with mean 4 and standard deviation 3 has the wider spread?

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