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.
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
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
[tex]\mu_1=3[/tex]
[tex]\sigma_1=4[/tex]
Second normal distribution has
[tex]\mu_2=4[/tex]
[tex]\sigma_2=3[/tex]
Since [tex]\sigma_1>\sigma_2[/tex], therefore the normal distribution with mean 3 and standard deviation 4 has a wider spread.
Hence the correct option is 1.