The production manager of Hinton Press is determining the average time needed to photograph one printing plate. Using a stopwatch and observing the platemakers, he collects the following times (in seconds):


20.4 20.0 22.2 23.8 21.3 25.1 21.2 22.9 28.2 24.3
22.0 24.7 25.7 24.9 22.7 24.4 24.3 23.6 23.2 21.0

An average per-plate time of less than 23.0 seconds indicates satisfactory productivity. Should the manager be concerned

Ans

To determine if the production manager should be concerned about the average time, we need to calculate the mean of the collected times and compare it to the threshold of 23.0 seconds.

Step 1: Calculate the mean
To calculate the mean, we sum up all the collected times and divide by the total number of observations.

Sum of the times: 20.4 + 20.0 + 22.2 + 23.8 + 21.3 + 25.1 + 21.2 + 22.9 + 28.2 + 24.3 + 22.0 + 24.7 + 25.7 + 24.9 + 22.7 + 24.4 + 24.3 + 23.6 + 23.2 + 21.0 = 463.8

Total number of observations: 20

Mean = Sum of the times / Total number of observations
Mean = 463.8 / 20
Mean = 23.19

Step 2: Compare the mean to the threshold
The mean calculated is 23.19 seconds. Since it is greater than the threshold of 23.0 seconds, the average time is not satisfactory, and the production manager should be concerned about the productivity.

Therefore, the manager should be concerned about the average time.

To determine whether the manager should be concerned, we need to calculate the average time needed to photograph one printing plate and compare it to the threshold of 23.0 seconds.

To calculate the average time, we add up all the times and divide by the number of observations.

Sum of times: 20.4 + 20.0 + 22.2 + 23.8 + 21.3 + 25.1 + 21.2 + 22.9 + 28.2 + 24.3 + 22.0 + 24.7 + 25.7 + 24.9 + 22.7 + 24.4 + 24.3 + 23.6 + 23.2 + 21.0 = 469.0

Number of observations: 20

Average time = Sum of times / Number of observations = 469.0 / 20 = 23.45 seconds.

The average time needed to photograph one printing plate is 23.45 seconds. Since it is greater than the threshold of 23.0 seconds for satisfactory productivity, the manager should be concerned.

In conclusion, the manager should be concerned about the productivity level based on the average time per plate.