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...
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 $\displaystyle \overline{X}$ ~ Normal $\displaystyle \left(\mu = 20, \sigma^2 = \frac{4}{5}\right)$.
So $\displaystyle \Pr\left( Z < \frac{K - 20}{\frac{2}{\sqrt{5}}}\right) = 0.3$.
So, although it's a bit hard to tell, it looks like you're right.