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

Answer:

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.