Respuesta :
Answer:
0.055
Step-by-step explanation:
We have been given that the probability of an employee receiving the Superstar of the Month Award for a large company is 22%. We are asked to find the probability of exactly 10 employees receiving the award out of one department with 30 employees.
We will use Bernoulli's trails to solve our given problem.
[tex]P(X=x)=^nC_x\cdot p^x(1-p)^{n-x}[/tex]
Upon substituting our given values, in above formula, we will get:
[tex]P(X=10)=^{30}C_{10}\cdot 0.22^{10}(1-0.22)^{30-10}[/tex]
[tex]P(X=10)=\frac{30!}{10!(30-10)!}\cdot 0.22^{10}(0.78)^{20}[/tex]
[tex]P(X=10)=\frac{30*29*28*27*26*25*24*23*22*21*20!}{10*9*8*7*6*5*4*3*2*20!}\cdot 0.0000002655992279\cdot 0.0069485158708622[/tex]
[tex]P(X=10)=29*3*13*5*23*11*21\cdot 0.00000000184552045035189[/tex]
[tex]P(X=10)=30045015\cdot 0.00000000184552045035189[/tex]
[tex]P(X=10)=0.055448689613[/tex]
[tex]P(X=10)\approx 0.055[/tex]
Therefore, the probability that exactly 10 employees will receive the award out of one department with 30 employees, would be 0.055.
