import math coeff_x = 1 coeff_y = 1

var_x = 9 var_y = 16

var = (coeff_x**2)*var_x + (coeff_y**2)*var_y

sd = math.sqrt(var)

print(round(sd,1))

The variance of the sum of two independent random variables X and Y is equal to the sum of their variances. That is, if X and Y are independent random variables, then:

sigma^2 {X+Y} = sigma^2(X) + sigma^2(Y).

The problem statements says both x, y are two independent "normal" random deviates: 3**2 + 4**2

Notice that the problem statement is incorrect. It is the variance of the sum of random variables, and not the sum of the distributions of the random variables. Distribution of a random variable !=random variable

http://www.stat.yale.edu/Courses/1997-98/101/rvmnvar.htm

For independent random variables X and Y, the variance of their sum or difference is the sum of their variances:

Variances are added for both the sum and difference of two independent random variables because the variation in each variable contributes to the variation in each case. If the variables are not independent, then variability in one variable is related to variability in the other. For this reason, the variance of their sum or difference may not be calculated using the above formula