# Math Help - problem of normal distribution

1. ## problem of normal distribution

i set up the equation P[ (X1+X2+...+X5)/5 < K ] = 0.3
then P[ z < ( 5K-(20)(5) )/ √(4)(5)] = 0.3
am i right???
if i am wrong, show me how to solve it please...

2. Originally Posted by kin

i set up the equation P[ (X1+X2+...+X5)/5 < K ] = 0.3
then P[ z < ( 5K-(20)(5) )/ √(4)(5)] = 0.3
am i right???
if i am wrong, show me how to solve it please...
Note that $\overline{X}$ ~ Normal $\left(\mu = 20, \sigma^2 = \frac{4}{5}\right)$.

So $\Pr\left( Z < \frac{K - 20}{\frac{2}{\sqrt{5}}}\right) = 0.3$.

So, although it's a bit hard to tell, it looks like you're right.