Answer
a. $0.021$
b. $0.0012$
c. $3.13\times10^{-7}$
d. The individual fail rate is low (0.05), higher probabilities will be for X=0 (0.77) and X=1 (0.204).
Work Step by Step
$p=0.05, n=5$
a. Exactly 2 will fail.
$P(X=2)=_5C_20.05^20.95^3=0.021$
b. More than 2 will fail.
$P(X\geq3)=1-P(X\leq2)=0.0012$
c. All will fail.
$P(X=5)=_5C_50.05^50.95^0=3.13\times10^{-7}$
d. Compare the answers for parts a, b, and c, and explain why these results are reasonable.
The individual fail rate is low (0.05), higher probabilities
will be for X=0 (0.77) and X=1 (0.204).
