Answer:
the probability that a guitar neck can be carved between 95 and 165 minutes is 7/8 or approximately 0.875.
Explanation:
We know that the time it takes to hand carve a guitar neck is uniformly distributed between 110 and 190 minutes. This means that the probability of carving a guitar neck between any two times is proportional to the length of that interval.
Let X be the time it takes to hand carve a guitar neck. Then X is uniformly distributed between 110 and 190 minutes, and we can write:
X ~ U(110, 190)
To find the probability that a guitar neck can be carved between 95 and 165 minutes, we need to find the probability that X is between 95 and 165:
P(95 < X < 165) = (165 - 95) / (190 - 110) = 70 / 80 = 7/8
Therefore, the probability that a guitar neck can be carved between 95 and 165 minutes is 7/8 or approximately 0.875.