Final answer:
To estimate the number of devices out of 560 that will need maintenance, a proportion 9/40 = x/560 is set up and solved to find that 126 devices will likely need maintenance.
Step-by-step explanation:
The student's question involves calculating a proportional prediction basing on the information that 9 out of 40 randomly chosen devices needed maintenance. To estimate the number of devices that will require maintenance out of 560, we can set up a proportion because the scenarios are similar, and we assume the probability of a device requiring maintenance remains the same.
We know that 9 out of 40 devices needed maintenance, which gives us the fraction 9/40. To find out how many out of 560 will need maintenance, we set this equal to x/560, where x represents the unknown number of devices needing maintenance.
The proportion is then:
9/40 = x/560
Cross-multiplying to solve for x gives:
9 * 560 = 40 * x
5040 = 40x
x = 5040 / 40
x = 126
Therefore, 126 devices will likely need maintenance out of 560.