Answer:
A) 0.1636
B) 0.7292
C) 0.0305
Step-by-step explanation:
This is a binomial probability distribution question that follows;
P(X = x) = nCx × p^(x) × q^(n - x)
In this case, p = 64% = 0.64
q = 1 - p = 1 - 0.64 = 0.36
Thus;
A) P(exactly 5) = P(5) = 10C5 × 0.64^(5) × 0.36^(10 - 5) = 0.1636
B) P(at least 6) = P(x ≥ 6) = P(6) + P(7) + P(8) + P(9) + P(10)
P(6) = 10C6 × (0.64^(6)) × (0.36^(10 - 6)) = 0.2424
P(7) = 10C7 × (0.64^(7)) × (0.36^(10 - 7)) = 0.2462
P(8) = 10C8 × (0.64^(8)) × (0.36^(10 - 8)) = 0.1642
P(9) = 10C9 × (0.64^(9)) × (0.36^(10 - 9)) = 0.0649
P(10) = 10C10 × (0.64^(10)) × (0.36^(10 - 10)) = 0.0115
Thus;
P(x ≥ 6) = 0.2424 + 0.2462 + 0.1642 + 0.0649 + 0.0115
P(x ≥ 6) = 0.7292
C) P(x < 4) = P(0) + P(1) + P(2) + P(3)
From online binomial probability calculator, we have;
P(x < 4) = 0.0305
