A brokerage survey reports that 30 per cent of individual investors have used a discount broker, that is, one which does not charge the full commission. In a random sample of 9 individuals, what is the probability that a. Exactly two of the sampled individuals have used a discount broker, b. Not more than three have used a discount broker, c. At least three of them have used a discount broker.
Answers
Given : A brokerage survey reports that 30 per cent of individual investors have used a discount broker
To Find : In a random sample of 9 individuals, what is the probability that
a. Exactly two of the sampled individuals have used a discount broker,
b. Not more than three have used a discount broker,
c. At least three of them have used a discount broker.
Solution:
30 per cent of individual investors have used a discount broker
=> p = 30/100 = 0.3
q = 1 - p = 1 - 0.3 = 0.7
n = 9
P(x) = ⁿCₓpˣqⁿ⁻ˣ
Exactly two of the sampled individuals have used a discount broker,
=> x = 2
P(2) = ⁹C₂(0.3)²(0.7)⁷ = 0.2668
b. Not more than three have used a discount broker
= P(0) + P(1) + P(2) + P(3)
= ⁹C₀(0.3)⁰(0.7)⁹ + ⁹C₁(0.3)¹(0.7)⁸ + ⁹C₂(0.3)²(0.7)⁷+ ⁹C₃(0.3)³(0.7)⁶
At least three of them have used a discount broker.
= 1 - P(0) - P(1) - P(2)
= 1- ⁹C₀(0.3)⁰(0.7)⁹ - ⁹C₁(0.3)¹(0.7)⁸ - ⁹C₂(0.3)²(0.7)⁷
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