Answer
Therefore, P(x < 3) = 0.9691
Work Step by Step
n = 15, p = 0.047, q = 0.953
binomial distribution formula ${n}\choose{x}$ $\cdot$ $p^{x} \cdot q^{n-x}$
P(x < 3)
= P(x = 0) + P(x = 1) + P(x = 2)
P(x = 0) = ${15}\choose{0}$ $\cdot$ $0.047^{0} \cdot 0.953^{15-0}$ $\approx$ 0.48573
P(x = 1) = ${15}\choose{1}$ $\cdot$ $0.047^{1} \cdot 0.953^{15-1}$ $\approx$ 0.35933
P(x = 2) = ${15}\choose{2}$ $\cdot$ $0.047^{2} \cdot 0.953^{15-2}$ $\approx$ 0.12404
Therefore, P(x < 3) = 0.48573 + 0.35933 + 0.12404 = 0.9691
