Answer
0.5793.
Work Step by Step
q=1-p=1-0.4=0.6
$n\cdot p=25\cdot 0.4=10\geq5.$
$n\cdot q=25\cdot 0.6=15\geq5.$
Hence, the requirements are satisfied.
mean: $\mu=n\cdotp=25\cdot0.4=10$
standard deviation: $\sigma=\sqrt{n\cdot p\cdot q}=\sqrt{25 \cdot0.4\cdot0.6}=\sqrt{6}=2.45.$
9.5 is the first one more than 9, hence:
$z=\frac{value-mean}{standard \ deviation}=\frac{9.5-10}{2.45}=-0.2.$
By using the table, the probability belonging to z=-0.2: 0.4207, hence the probability of z being more than 0.2: 1-0.4207=0.5793.
