Respuesta :
Answer:
The probability that in two square yards of screens, there will be 4 flaws is 0.1954.
Step-by-step explanation:
Let X = number of flaws per square yard.
The average number of flaws per square yard is, λ = 2.
The random variable X follows a Poisson distribution with parameter λ = 2.
The probability mass function of a Poisson random variable is:
[tex]P(X=x)=\frac{e^{-2}2^{x}}{x!};\ x=0,1,2,3...[/tex]
The average number of flaws in 1 square yard is, 2.
Then the average number of flaws in 2 square yard is, 2 × 2 = 4 = λ.
Compute the probability that in two square yards of screens, there will be 4 flaws as follows:
[tex]P(X=4)=\frac{e^{-4}4^{4}}{4!}\\=\frac{0.01832\times256}{24}\\=0.1954[/tex]
Thus, the probability that in two square yards of screens, there will be 4 flaws is 0.1954.
Answer:
Probability that in two square yards of screens, there will be 4 flaws is 0.01221 .
Step-by-step explanation:
We are given that Screens used in screen doors typically have 2 flaws per square yard.
Let X = Distribution of Number of flaws
Let the average number of flaws per square yard = [tex]\lambda[/tex] = 2
So, X will have Poisson distribution such that;
X ~ Poisson([tex]\lambda = 2[/tex])
The Probability distribution function of Poisson distribution is given by;
P(X = x) = [tex]\frac{e^{-\lambda}*\lambda^{x} }{x!}[/tex] where, x = 0,1,2,3,.....
So, here in two square yards of screens, the average number of flaws = 2 *2 = [tex]\lambda =[/tex] 4
So, Probability that in two square yards of screens, there will be 4 flaws =
P(X = 4) = [tex]\frac{e^{-4}*4^{4} }{4!}[/tex] = [tex]\frac{e^{-4}*16 }{4*3*2*1}[/tex] = 0.01221 .
