Question

If X and Y are 2 independent normal variables with mean as 10 and 12 and SD as 3 and 4, then (X+Y) is normally distributed with
(a) mean = 22 and SD = 7
(b) mean = 22 and SD = 25
(c) mean = 22 and SD = 5
(d) mean = 22 and SD = 49​

Answer 1

Answer:

(c)

Step-by-step explanation:

Mean(X+Y) = Mean(X) + Mean(Y) = 10+12 = 22

SD(X+Y) =

$\sqrt{sd(x)^{2} + sd(y)^{2} }$

=

$\sqrt{ {3}^{2} + {4}^{2} }$

= 5