Suppose nonconforming parts are produced with a rate = 8 / hour (i. e. on average, 8 nonconforming parts will be made during a production period of one hour). (a) If x denotes the number of nonconforming parts made during one hour, what distribution does x follow? Please define the parameter(s) needed for defining the distribution based on the information provided.
(b) What is the probability that exactly 5 nonconforming parts are produced during a 1-hour period? What is the probability that at least 5 nonconforming parts are produced during a 1-hour period?
(c) What are the expected value and standard deviation of the number of nonconforming parts produced during a 120-min period?
(d) What is the probability that at least 20 nonconforming parts produced during a 2.5-hour period? That at most 10 nonconforming parts produced during this period?

(a)   x follows a poisson distribution with parameter λ = 8 / hour

(b)   P( X = 5 ) = 0.09160

      P( X ≥ 5 ) = 0.9004

(c)   the expected value  of the number of nonconforming parts produced during a 120-min period = 16 nonconforming parts per 120 minutes

The standard deviation = 4

(d)   P(X ≥ 20) = 0.5297

      P( X ≤  10) = 0.0108

Step-by-step explanation:

Suppose nonconforming parts are produced with a rate = 8 / hour (i.e. on average, 8 nonconforming parts will be made during a production period of one hour).

(a)  If x denotes the number of nonconforming parts made during one hour, then : x follows a poisson distribution with parameter λ = 8 / hour

(b)

What is the probability that exactly 5 nonconforming parts are produced during a 1-hour period? What is the probability that at least 5 nonconforming parts are produced during a 1-hour period?

the probability that exactly 5 nonconforming parts are produced during a 1-hour period can  be computed as:

P( X = 5 ) =

P( X = 5 ) =

P( X = 5 ) = 0.09160

the probability that at least 5 nonconforming parts are produced during a 1-hour period

P( X ≥ 5 ) = 1 -  P( X ≤ 4)

P( X ≥ 5 ) = 0.9004

c)  What are the expected value and standard deviation of the number of nonconforming parts produced during a 120-min period?

the expected value  of the number of nonconforming parts produced during a 120-min period

= 16 nonconforming parts per 120 minutes

The standard deviation =

The standard deviation =

The standard deviation = 4

(d) What is the probability that at least 20 nonconforming parts produced during a 2.5-hour period? That at most 10 nonconforming parts produced during this period?

During a 2.5 - hour period , the expected value = 8 × 2.5 = 20

As such, the probability  that at least 20  nonconforming parts produced during a 2.5-hour period is:

P(X ≥ 20) = 1 - P(X ≤ 19)

P(X ≥ 20) = 1 -  0.4703

P(X ≥ 20) = 0.5297

Probability that at most  10 nonconforming parts produced during this period is:

P( X ≤  10) =

P( X ≤  10) = 0.0108

understand that i don't know the answers

will someone answer his question

go on the tube you might find some information there