Respuesta :
Answer:
The probability of successes P( x < 4 ) = 0.36138
Step-by-step explanation:
Step(i):-
Given 'n'=9
The probability of success 'p' = 0.45
q = 1-p = 1-0.45 = 0.55
Let 'X' be the random variable in Binomial distribution
[tex]P(X=r) = n_{C_{r} } p^{r} q^{n-r}[/tex]
[tex]n_{C_{r} } = \frac{n!}{(n-r)!r!}[/tex]
Step(ii):-
The probability of x successes in the n independent trials of the experiment
[tex]P(x<4) = P(x=0) +P(x=1)+P(x=2)+P(x=3)[/tex]
= [tex]= 9_{C_{0} } (0.45)^{0} (0.55)^{9-0}+9_{C_{1} } (0.45)^{1} (0.55)^{9-1}+9_{C_{2} } (0.45)^{2} (0.55)^{9-2}+9_{C_{3} } (0.45)^{3} (0.55)^{9-3}[/tex]By using factorial notation
[tex]n_{C_{r} } = \frac{n!}{(n-r)!r!}[/tex]
[tex]9_{C_{0} } = 1 , 9_{C_{1} } = 9 , 9_{C_{2} } = 36, 9_{C_{3} } = 84[/tex]
P( x < 4 ) = (0.55)⁹ + 9(0.45) (0.55)⁸ + 36 (0.45)² (0.55)⁷ +84 (0.45)³ (0.55)⁶
P( x < 4 ) = 0.004605+0.03391 + 0.1109855+ 0.21188
P( x < 4 ) = 0.36138
Final answer:-
The probability of successes P( x < 4 ) = 0.36138
