Respuesta :
Answer:
(A) 0.999996
(B) 0.11680
Step-by-step explanation:
We are given that a Randstad Harris interactive survey reported that 25% of employees said their company is loyal to them.
And 9 employees are selected randomly and interviewed about company loyalty.
The Binomial probability distribution is given by;
[tex]P(X=r)= \binom{n}{r}p^{r}(1-p)^{n-r} for x = 0,1,2,3,....[/tex]
where, n = number of trials (samples) taken
r = number of success
p = probability of success
In our question; n = 9 , p = 0.25 (as employees saying their company is loyal to them is success to us)
(A) Probability that none of the 9 employees will say their company is loyal to them = 1 - Probability that all 9 employees will say their company is loyal to them
= 1 - P(X = 9) { As here number of success is 9 }
= 1 - [tex]\binom{9}{9}0.25^{9}(1-0.25)^{9-9}[/tex] = 1 - [tex]0.25^{9}[/tex] = 0.999996
(B) Probability that 4 of the 9 employees will say their company is loyal to them = P(X = 4)
P(X = 4) = [tex]\binom{9}{4}0.25^{4}(1-0.25)^{9-4}[/tex]
= [tex]126*0.25^{4}*0.75^{5}[/tex] = 0.11680
