Elementary Statistics (12th Edition)

a) $P(X=8)={8\choose 8} \cdot (0.9)^8\cdot (0.1)^0=0.43.$ b)$P(X=7)={8\choose 7} \cdot (0.9)^7\cdot (0.1)^1=0.383.$ c)$P(X\geq7)=P(X=7)+P(X=8)={8\choose 7} \cdot (0.9)^7\cdot (0.1)^1+{8\choose 8} \cdot (0.9)^8\cdot (0.1)^0=0.383+0.43=0.813$ d) No, it is not an unusually high probability, because 0.813 is really high, more than 0.05.