Dynamic random-access memory (DRAM) memory chips are made from silicon wafers in manufacturing facilities through a very complex process called wafer fabs. The wafers are routed through the fab machines in an order that is referred to as a recipe. The wafers may go through the same machine several times as the chip is created. The data file DRAM Chips
Download DRAM Chips
contains a sample of processing times, measured in fractions of hours, at a particular machine center for one chip recipe.

Compute the mean processing time.

Question

Dynamic random-access memory (DRAM) memory chips are made from silicon wafers in manufacturing facilities through a very complex process called wafer fabs. The wafers are routed through the fab machines in an order that is referred to as a recipe. The wafers may go through the same machine several times as the chip is created. The data file DRAM Chips 
Download DRAM Chips
contains a sample of processing times, measured in fractions of hours, at a particular machine center for one chip recipe.

Compute the mean processing time.

BlackTom AI · Accepted Answer

To tackle this question, I start by restating what is being asked and what information is available. The problem asks to compute the mean processing time for DRAM chip fabrication, given that the times are measured in fractions of hours and that a data file titled DRAM Chips contains a sample of processing times at a particular machine center for one chip recipe. The answer options present times in minutes. However, the actual numeric data values from the sample are not provided in the prompt, so a precise numerical mean cannot be computed from what is given here.

Option 0.22 minutes: This value is expressed in minutes, but since the data are described as fractions of hours, any mean derived from those data would originally be in hours. If one were to convert a mean from hours to minutes, multiply by 60. Therefore, 0.22 minutes would correspond to 0.003666... hours, which is a very small mean in the context of wafer processing times. Whether this is plausible depends entirely on the actual sample values; without them, we cannot verify.

Option 0.24 minutes: Like the previous option, this is a small number in minutes. Converting back, 0.24 minutes equals 0.004 hours. This would imply an extremely short mean processing time per operation, which seems unlikely for wafer fabrication steps that typically involve longer durations. Yet again, verification requires the sample data values.

Option 0.33 minutes: This is another small-minute value. Converting to hours, 0.33 minutes is 0.0055 hours. As with the prior two options, the plausibility depends on the actual sample; however, given that the times are specified as fractions of hours, any mean presented in minutes must be consistent with a corresponding mean in hours when back-converted.

Option 0.31 minutes: This is slightly larger than the other minute-based choices, equating to 0.005166... hours. The same unit-consistency check applies: the mean in hours would be this value divided by 60, and you’d need the original hour-based mean to assess plausibility.

Key conceptual point: when data are stated as fractions of hours, the natural unit for the mean is hours. If a question wants the mean shown in minutes, you must convert the mean hours to minutes by multiplying by 60. Any presented value in minutes should correspond to 60 times the mean in hours. Since the actual sample values are not provided here, we cannot perform the conversion and compute the exact numeric mean.

Another important consideration is whether the problem statement’s wording implies that the mean should be reported in minutes after converting from hours, or whether the raw mean in hours is what should be reported. The discrepancy between the data unit (fractions of hours) and the answer options (minutes) creates a need to clarify the expected unit of the final result before performing any calculation.

In summary, due to the absence of the actual sample data values, a precise mean cannot be determined from the information given. The presence of minute-based options suggests a unit conversion step is expected, but without the underlying hour-based mean, we cannot verify which of these options, if any, correctly represents the mean. The key pitfall to avoid is reporting a mean in minutes without ensuring it aligns with the hour-based nature of the data after applying the correct 60-minute-per-hour conversion.

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