Answer
0.0794
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: $\sigma=\sqrt{n\cdot p\cdot q}=\sqrt{100\cdot0.22\cdot0.78}=\sqrt{3.12}=4.14.$
19 is between 19.5 and 18.5, hence:
$z_{1}=\frac{value-mean}{standard \ deviation}=\frac{19.5-22}{4.14}=-0.6.$
$z_{2}=\frac{value-mean}{standard \ deviation}=\frac{18.5-22}{4.14}=-0.84.$
By using the table, the probability belonging to z=-0.6: 0.2743, to z=-0.84: 0.1949, hence the probability: 0.2743-0.1949=0.0794.
