Answer
0.2743.
Work Step by Step
q=1-p=1-0.78=0.22
$n\cdot p=100\cdot 0.22=22\geq5.$
$n\cdot q=100\cdot 0.78=78\geq5.$
Hence, the requirements are satisfied.
mean: $\mu=n\cdotp=100\cdot0.22=22$
standard deviation: $\sigma=\sqrt{n\cdot p\cdot q}=\sqrt{100 \cdot0.22\cdot0.78}=\sqrt{6}=4.14.$
19.5 is the first one less than 20, hence:
$z=\frac{value-mean}{standard \ deviation}=\frac{19.5-22}{4.14}=-0.604.$
By using the table, the probability belonging to z=-0.604: 0.2743.
