1. Disks of polycarbonate plastic from a supplier were analyzed for scratch and
ID: 3062997 • Letter: 1
Question
1. Disks of polycarbonate plastic from a supplier were analyzed for scratch and shock resistance. Parts were then characterized as being "high" or “low" for each category and the following joint probability distribution was developed Shock resistanceShock resistance High Scratch Resistance High Low Low 03 06 03 A disk is acceptable for production only if scratch and shock resistance are rated as "high". a. A case of 24 such disks is purchased. What is the probability that at least one of the disks are not acceptable for production? Assume part-to-part independence (one disk's chance of being unacceptable is independent of any other disks being unacceptable) b. A disk is acceptable for production only if scratch and shock resistances are rated as "high". 5000 each disks are purchased. Let random variable Y= the number of disks that was acceptable for production. Find E[Y One disk is selected and it is determined that has low scratch resistance What is the probability that it will also have low shock resistance? c.Explanation / Answer
a. Probability that a disk is acceptable = 0.88
The distribution of acceptable disks, X ~ Binom(24,0.88)
Probability that 0 disks are not acceptable = Probability that all 24 disks are acceptable = C[24,24] x 0.8824x 0.120 = 0.0465
Probability that at least 1 disk is not acceptable = 1 - Probability that 0 disks are not acceptable = 1-0.0465 = 0.9535
(b) Y ~ Binom(5000,0.88)
E[Y] = 5000 x 0.88 = 4400
(c) Probability of a disk to have low scratch resistance = 0.03+0.06 = 0.09
Probability of the disk having low shock resistance, given that it has low shock resistance = 0.06/0.09 = 2/3 =0.6667
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