Answer
0.0928.
Work Step by Step
q=1-p=1-0.78=0.22$
$n⋅p=100⋅0.22=22≥5.$
$n⋅q=100⋅0.78=78≥5.$
Hence, the requirements are satisfied.
mean: $\mu=n\cdotp=100\cdot0.22=22.$
standard deviation: $\sigma=\sqrt{n\cdot p\cdot q}=\sqrt{100\cdot0.22\cdot0.78}=\sqrt{3.12}=4.14.$
23 is between 23.5 and 22.5, hence:
$z_{1}=\frac{value-mean}{standard \ deviation}=\frac{22.5-22}{4.14}=0.12.$
$z_{2}=\frac{value-mean}{standard \ deviation}=\frac{23.5-22}{4.14}=0.36.$
By using the table, the probability belonging to z=0.36: 0.6406, to z=0.12: 0.5478, hence the probability: 0.6406-0.5478=0.0928.
