Question

Practice Questions 5) Company A produces wings for commercial drones. After having a great fire disaster at the company, they lost all their equipments and machines. Therefore, they just bought a new machine that produces wings much faster, however the machine glitches 6 times every 24 hours. a. The operator initiated the machine for 2 hour period. What is the probability that the machine won't glitch in 2 hour period ? b. What is the probablity that the machine will glitch two times in the next 5 hours ? c. The company could compansate the machine having a glitch once, but anymore within a sitting commpany loses money. What is the probability that the machine will not glitch in the next 5 hour period ?

Answer 1

The given scenario is of Poisson Process.

The machine glitches 6 times in 24 hours.

So the

X= 6 in 24hrs

in 1 hour , $\lambda =\frac{6}{24}=0.25$

So the rate of glitches

X=0.25 per hour

Now for Poisson Process we have $P(X(t)=x)= \frac{e^{-\lambda t}\cdot {(\lambda t)}^x}{x!}$ , Her the random variable is

,which denotes the number of glitches at time t.

X(t)

a.) and
X=0.25 per hour
.

We have

$P(X(2)=0)= \frac{e^{-(0.25\times 2)}\cdot {(0.25\times 2)}^x}{0!}=e^{-0.5}=0.6065$

The probability of zero glitches in 2 hours is 0.6065.

b) Now, and
X=0.25 per hour
. We have

$P(X(5)=2)= \frac{e^{-(0.25\times 5)}\cdot {(0.25\times 5)}^2}{2!}=\frac{e^{-1.25}(1.25)^2}{2}=0.2238$

The probability that the machine will have two glitches in 5 hours is 0.2238.

c)

and
X=0.25 per hour
.

We have

$P(X(5)=0)= \frac{e^{-(0.25\times 5)}\cdot {(0.25\times 5)}^0}{0!}=e^{-1.25}=0.2865$

The probability that the machine will not glitch in 5 hours is 0.2865.