Respuesta :
Answer:
0.84882
Step-by-step explanation:
Given:-
The production process is in control is number of chocolate chips in a cookie. The mean number of chocolate chips per cookie is 6.0.
λ = 6.0
- We define a random variable (X) that denotes the number of chocolate chips inspected on a cookie follows a poisson distribution:
X ~ Po ( 6.0 )
Find:-
how many cookies should the manager expect to discard from the batch if the policy is that each cook must have at least four chocolate chips?
Solution:-
- We will use the probability mass function of Poisson variate (X). Given:
[tex]P ( X = x) = \frac{lambda^k*e^-^l^a^m^b^d^a}{k!} \\\\P ( X = x) = \frac{6^k*e^-^6}{k!}[/tex]
Where, k = 0 , 1 , 2 , 3 , 4 , 5 , 6 , .... , n = 100
- The required probability is P ( X ≥ 4 ); Using the pmf function we have:
[tex]P ( X \geq 4 ) = 1 - P ( X < 4 )\\\\P ( X \geq 4 ) = 1 - [ \frac{6^0*e^-^6}{0!} + \frac{6^1*e^-^6}{1!} + \frac{6^2*e^-^6}{2!} + \frac{6^3*e^-^6}{3!} ]\\\\P ( X \geq 4 ) = 1 - [ 0.00247 + 0.01487 + 0.04461 + 0.08923 ]\\\\P ( X \geq 4 ) = 1 - [ 0.15118 ] = 0.84882[/tex]
