Question

An economist in Kenya argued that 3.5% of all SMES would file for bank loans next year. For a random sample of 100SMES estimate the probability that at least 3 will file bank loans next year

Answer 1

Answer: 0.6841

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 :

`P(X=x)=^nC_xp^x(1-p)^(n-x)`

The probability that at least 3 will file bank loans next year :

`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`

Hence, the required probability= 0.6841