The time it takes a worker on an assembly line to complete a task is exponentially distributed with a mean of 8 minutes. What is the probability that it will take a worker less than 4 minutes to complete the task

The probability is

Step-by-step explanation:

We know that the time it takes a worker on an assembly line to complete a task is exponentially distributed with a mean of 8 minutes.

Let's define the random variable ⇒

'' The time it takes a worker on an assembly line to complete a task ''

We know that is exponentially distributed with a mean of 8 minutes ⇒

~ Exp (λ)

Where '' λ '' is the parameter of the distribution.

Now, the mean of an exponential distribution is ⇒

1 / λ  (I)

We have the value of the mean '' '' , then we replace that value in the equation (I) to obtain the parameter λ ⇒

1 / λ  ⇒

λ =

Then ,   ~

The cumulative distribution function of is :

when and

1 - e ^ ( - λx) when (II)

If we replace the value of the parameter in (II) :

 when

We need to calculate

Given that is a continuous random variable :

We use the cumulative distribution function to calculate the probability :

The probability is

dnji

step-by-step explanation:

dskfbipo

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)