Question

A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two. What is the probability of no defects in 10 feet of steel

Answer 1

Answer:

the probability of no defects in 10 feet of steel = 0.1353

Step-by-step explanation:

GIven that:

A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.

Let consider β to be the average value for defecting

So;

β = 2

Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.

Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2

i.e

$Y \sim P( \beta = 2)$

the probability mass function can be represented as follows:

$\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}$

where;

y =  0,1,2,3 ...

Hence,  the probability of no defects in 10 feet of steel

y = 0

$\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}$

$\mathtt{P(y =0) = \dfrac{0.1353 \times 1}{1}}$

P(y =0) = 0.1353