Peter I. answered • 06/25/13

Tutoring for Scholastic Excellence in Business and Science

There are two parts to the question.

Only two possible scenarios: a) success or b) failure

Applying the binomial concept:

P(satisfaction) = 80% or 0.8; P(dissatisfaction) = 20% or 0.2

Therefore, P(9 or more satisfied persons) = P(9) + P(10) + P(11) + P(12)

**1st part**

= 12C9 * (0.8)^9 * (0.2)^3 + 12C10 * (0.8)^10 * (0.2)^2 + 12C11 * (0.8)^11 * (0.2)^1 + 12C12 * (0.8)^12 * (0.2)^ 0

= 0.2362 + 0.2835 + 0.2062 + 0.0687

= 0.7946 (1st part of the puzzle)

**2nd part**.

Solve for p(3, 4, 5, and 6 satisfied persons)

12C3*(0.8)^3 * (0.2)^9 + 12C4*(0.8)^4 * (0.2)^8 + 12C5*(0.8)^5 * (0.2)^7 + 12C6* (0.8)^6* (0.2)^6

= 0.00005767 + 0.00051904 + 0.0033219 + 0.0154995

= 0.01940