Question

A machine shop produces heavy duty high endurance 20-inch rods that are meant for use in a variety of military grade equipment. On occasion, the machine malfunctions and produces a groove or a chisel cut mark somewhere on the rod. If such defective rods can be cut so that there is at least 15 consecutive inches without a groove, then the rods can be salvaged for other purposes. If the location of the groove on a rod is described by a uniform distribution, what is the probability that a defective rod can be salvaged?

Answer 1

The probability that a defective rod can be salvaged = 0.50

Explanation:

Given that:

A machine shop produces heavy duty high endurance 20-inch rods

On occasion, the machine malfunctions and produces a groove or a chisel cut mark somewhere on the rod.

If such defective rods can be cut so that there is at least 15 consecutive inches without a groove.

Then; The defective rod can be salvaged if the groove lies on the rod between 0 and 5 inches i.e ( 20 - 15 )inches

Now:

P(X ≤ 5) =
`(5)/(20)`

= 0.25

P(X ≥ 15) =
`(5)/(20)`

= 0.25

The probability that a defective rod can be salvaged = P(X ≤ 5) + P(X ≥ 15)

= 0.25+0.25

= 0.50

∴ The probability that a defective rod can be salvaged = 0.50