Answer: 0.6841
Step-by-step explanation:
Given: Probability of all SMES would file for bank loans next year = 3.5% = 0.035
Sample size : n = 100
Binomial probability distribution formula :
[tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]
The probability that at least 3 will file bank loans next year :
[tex]P(x\geq3)=1-P(x<3)\\\\=1-(P(x=0)+P(x=1)+P(x=2))\\\\=1-(^{100}C_0(0.035)^0(1-0.035)^{100}+\ ^{100}C_1(0.035)^1(1-0.035)^{99}+^{100}C_2(0.035)^2(1-0.035)^{98})\\\\=1-(0.3159)\\\\=0.6841[/tex]
Hence, the required probability= 0.6841
