If the average service rate is 12 minutes per customer, and assuming the negative exponential distribution is used to describe the randomness of the service time distribution, then determine the probability that the service time will be less than or equal to 10 minutes.

a. 0.624
b. 0.565
c. 0.283
d. 0.000

b. 565

Probability that service time will be less than or equal to 10 minutes is P = 0.5654.

Step-by-step explanation:

Data Given are as follows,

Service time

Average service rate  

First of all, as here average service rate is given as 12 minutes per customer

Using concept of Queuing Theory, as it is case of probability of service time less than or equal to T.

In addition, it is given that negative exponential distribution is assumed to describe the randomness of the service time distribution.

So it is given by,

            where P = probability that the service time will be less than T

                        β = average service rate in per minutes

                        T = service time in minutes

It can be solved by

Hence, from above analysis, it an be finally concluded that probability that service time will be less than or equal to 10 minutes is P = 0.5654.

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: