Do you dislike waiting in line? Supermarket chain Kroger has used computer simulation and information technology to reduce the average waiting time for customers at stores. Using a new system called QueVision, which allows Kroger to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just seconds (InformationWeek website and The Wall Street Journal website, January , ). a. Which of the exponential probability distribution is applicable and Show the probability density function of waiting time at Kroger. a. for b. for c. for d. for b. What is the probability that a customer will have to wait between and seconds (to 4 decimals)? c. What is the probability that a customer will have to wait more than minutes (to 4 decimals)?

The Complete question is shown in the explanation below and the solution is given in the picture attached

Step-by-step explanation:

Do you dislike waiting in line? Supermarket chain Kroger has used computer simulation and information technology to reduce the average waiting time for customers at 2300 stores. Using a new system called QueVision, which allows Kroger to better predict when shoppers will be checking out, the company was able to decrease average customer wait­ing time to just 26 seconds (information Week website and the Wall Street Journal web­ site, January 5, 2015).

a) Assume that Kroger waiting times are exponentially distributed. Show the probability density function of waiting time at Kroger.

b) what is the probability that a customer will have to wait between 15 and 30 seconds?

c) what is the probability that a customer will have to wait more than 2 minutes?

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.