The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability of assembling the product in less than 6 minutes is

Question

BlackTom AI · Accepted Answer

The question asks about the probability of completing the assembly in less than 6 minutes when the assembly time is uniformly distributed between 6 and 10 minutes. 
Option by option analysis will clarify common misunderstandings:

Option 1: 'zero' — This is correct given the distribution's support starts at 6 minutes. For a continuous uniform distribution on [6, 10], there is no probability mass below 6, so P(X < 6) = 0.

Option 2: '0.15' — This would suggest some positive probability below 6, which contradicts the fact that the smallest possible time in the model is 6 minutes. Since values strictly less than 6 are impossible, 0.15 cannot be correct.

Option 3: '0.50' — A value like 0.50 would correspond to the median being at 6 if the distribution were skewed, or to a point at which half of the probability lies below it. However, for a uniform distribution on [6, 10], P(X < 6) is not 0.5; in fact, it's 0 because 6 is the lower bound. This shows a common mix-up with the 50th percentile, which in this case is at 8.

Option 4: '1' — Claiming the probability is 1 would mean the event occurs with certainty for all outcomes, which cannot be the case here since the time can take values up to 10 minutes. Therefore P(X < 6) cannot be 1.

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability of assembling the product in less than 6 minutes is

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