Question

Need some guidance through this question:

A tool-and-die machine shop produces extremely high-tolerance spindles. The spindles are 18-inch slender rods used in a variety of military equipment. A piece of equipment used in the manufacture of the spindles malfunctions on occasion and places a single gouge somewhere on the spindle. However, if a defective spindle can be cut so that it has 14 consecutive inches without a gouge, then it can be salvaged for other purposes. Assume that the location of the gouge along a defective spindle is random, i.e., the distance of the location of the gouge from one end of the spindle is uniformly distributed over the interval (0, 18).

If 10 defective spindles are randomly selected, what is the probability that at least 6 cannot be salvaged?

Answer 1

P(a defective spindle can't be salvaged) = 1 - P(a defective spindle can be salvaged)

For a spindle to be salvaged, then the gouge should be present within 4 inches from either end.

So, probability that the gouge is present within 4 inches from either end = (2*4)/Total length = (2*4)/18 = 0.444444

Thus,

P(a defective spindle can be salvaged) = 0.44444

So,

P(a defective spindle can't be salvaged) = 1-0.44444 = 0.555556

X = number of spindles that cannot be salvaged

X follow binomial distribution with n = 10 , p = 0.55555

we need to find

P(X >= 6)

= 0.51884