# LOL very interesting GMAT case

• Jun 5th 2010, 04:09 AM
Nobelman
One of production steps for a company that makes equipment for the semiconductor industry involves polishing.The polishing machine requires a polishing disk.The amount of time this disk lasts vary from disk to disk.Once a disk wears to a certain point,it must be replaced with a new one.Experience indicates that the time to failure is exponentially distributed with a mean of 4.5 hours.The operators are required to log the amount of time each disk lasts.One operator reported the following times for her machine on her 12 hour shift: 2.4 hours, 1.5 hours,2.8 hours,and 3.1 hours(Note,the fifth disk was still okay when she went off shift after 12 hours).
A) For each of the four disks that were replaced,determine the probability that the disk will wear out in that number of hours or less.
HERE I found:
p(x<<1.5)= 0.283469
p(x<<2.8)=0.46325
p(x<<3.1)=0.497866

B)What is the probability that an operator would find 4 successive disks with these hours of performance?

C) Based on your answer to parts A and B, comment on whether you think there is evidence to suggest that the disks currently being used are not meeting the 4.5 hour mean life

P.S I cant still figure out how to solve the b and c))
Would be very nice if someone help!!
Further thanks!!!)))
• Jun 5th 2010, 10:23 AM
SpringFan25
(b)
the probability of observing exactly those hours is zero, because its a continuous variable.

Presumably the question means (what is the probability that you'd observe a disk with less than 1.6, then a disk with less than 2.8, then a disc with less than 3.1

In this case just multiply your probabilities together.

that should enable you to answer (c). Because part (b) is effectively a hypothesis test.
• Jun 5th 2010, 11:10 AM
Nobelman
Omg thank you very much!! You are genious :d:d:d