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

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

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) = (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) = (e^(- 2) \ 2^ \ 0)/(0!)}`

`\mathtt{P(y =0) = (0.1353 * 1)/(1)}`

P(y =0) = 0.1353