Answer
P(x < 3) = 0.4752
Work Step by Step
Using the binomial 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) = ${10}\choose{0}$ $\cdot$ $0.267^{0} \cdot 0.733^{10-0}$ = 0.00478
P(x = 1) = $ {10}\choose{1}$ $\cdot$ $0.267^{1} \cdot 0.733^{10-1}$ = 0.1631
P(x =2) = ${10}\choose{2}$ $\cdot$$0.267^{2} \cdot 0.733^{10-2}$ = 0.26729
Therefore, P(x < 3) = 0.04478 + 0.1631 + 0.26729 = 0.4752
