Answer
0.2743
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: $\sigma=\sqrt{n\cdot p\cdot q}=\sqrt{100\cdot0.22\cdot0.78}=\sqrt{3.12}=4.1425.$ 24.5 is the first one less than 25, hence: $z=\frac{value-mean}{standard \ deviation}=\frac{24.5-22}{4.1425}=0.6.$ By using the table, the probability belonging to z=0.6: 0.7257, hence the probability of z being more than 0.6: 1-0.7257=0.2743.
