Question

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?

Answer 1

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

Explanation:

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

`Z=(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.