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: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.