The weekly capacity measured in machine hours for a small machine shop follows the probability distribution shown below:

Use the following random numbers to simulate weekly capacity for the machine shop for the next five weeks: 93,31,71,8,6.
If the first random number interval begins with 1,then the minimum capacity for the simulated five week period is
A)560.
B)520.
C)440.
D)400.

Question

The weekly capacity measured in machine hours for a small machine shop follows the probability distribution shown below:

Use the following random numbers to simulate weekly capacity for the machine shop for the next five weeks: 93,31,71,8,6.
If the first random number interval begins with 1,then the minimum capacity for the simulated five week period is
A)560. 
B)520. 
C)440. 
D)400.

Quizplus · Accepted Answer

To simulate the weekly capacities for the next five weeks using the given random numbers, we simply match each random number with the corresponding interval of the probability distribution.

Week 1: Random number 93 falls in the interval 91-100, which corresponds to a capacity of 500 machine hours. 
Week 2: Random number 31 falls in the interval 21-30, which corresponds to a capacity of 200 machine hours. 
Week 3: Random number 71 falls in the interval 61-70, which corresponds to a capacity of 400 machine hours. 
Week 4: Random number 8 falls in the interval 1-10, which corresponds to a capacity of 100 machine hours. 
Week 5: Random number 6 falls in the interval 1-10, which corresponds to a capacity of 100 machine hours.

Therefore, the total capacity for the five week period is 500 + 200 + 400 + 100 + 100 = 1300 machine hours.

If the first random number interval begins with 1, then the minimum capacity would be 100 machine hours (the lowest capacity in the distribution). Thus, the minimum total capacity for the five week period would be 5 * 100 = 500 machine hours.

Therefore, the best answer choice is C, 440, as it is the only option less than the calculated minimum total capacity of 500 machine hours.

The Weekly Capacity Measured in Machine Hours for a Small