Answer :
The probability that precisely two of the sampled people utilized a discount broker is 0.2668.
A discount broker was employed by 30% of individual investors.
p = 30 ÷ 100 = 0.3
q = 1 - p
q = 1 - 0.3
q = 0.7
n = 9
P(x) = [tex]{}^{n}C_{x}p^{x}q^{n - x}[/tex]
Only two of the people polled had utilized a broker.
x = 2
P(2) = [tex]{}^{9}C_{2}[/tex](0.3)²[tex](0.7)^{7}[/tex]= 0.2668
Only three persons have used a deal broker.
= P(3) + P(2) + P(1) + P(0)
= [tex]{}^{9}C_{3}[/tex](0.3)³[tex](0.7)^{6}[/tex] + [tex]{}^{9}C_{2}[/tex](0.3)²[tex](0.7)^{7}[/tex] + [tex]{}^{9}C_{1}[/tex](0.3)¹[tex](0.7)^{8}[/tex] + [tex]{}^{9}C_{0}[/tex](0.3)⁰[tex](0.7)^9[/tex]
= (84 × 0.027 × 0.1176) + (36 × 0.09 × 0.0823) + (9 × 0.3 × 0.0576) + (1 × 1 × 0.0403)
= 0.7291
Probability of a broker has been employed by at least three of them.
= P(2) - P(1) - P(0) - 1
= -([tex]{}^{9}C_{2}[/tex](0.3)²[tex](0.7)^{7}[/tex] - [tex]{}^{9}C_{1}[/tex](0.3)¹[tex](0.7)^{8}[/tex] - [tex]{}^{9}C_{0}[/tex](0.3)⁰[tex](0.7)^9[/tex] - 1)
= -((36 × 0.09 × 0.0823) - (9 × 0.3 × 0.0576) - (1 × 1 × 0.0403) - 1)
= 0.9291
Learn more about probability at
https://brainly.com/question/28371185?referrer=searchResults
#SPJ4
