The specifications of aluminum rods for the length and the diameter are given. F
ID: 3319321 • Letter: T
Question
The specifications of aluminum rods for the length and the diameter are given. For each rod, the too long, or OK, and the diameter is classified as too thin, too is classified as too or OK. In a population of 1000 rods, th mber of rods in each class is as follows: Length,Diane ter Too Thin | OK | Too Thick Too short OK Too long 10 38 900 25 13 (a) A rod is sampled at random from this population. What is the probability that it is too short? (i) 10/1000 ) 3/101iv) 18/1000 short or too thick? (i) 5/1000(ii) 35/1000 ii 30/1000 40/1000 (b) A rod is sampled at random from this population. What is the probability that it is either too (c) What is the probability that the diameter is OK given that the length is too long? (i) 0.025 0.040 0.625 (iv) 0.0629Explanation / Answer
a) Probability that the rod is too short
= Number of too short rods / 1000
= 18 / 1000
Therefore (iv) is the required probability here.
b) Probability that the rod is either too short or too thick is computed here as:
= ( 10 + 3 + 5 + 4 + 13 ) / 1000
= 35 /1000
Therefore (ii) is the required probability here.
c) Given that the length is too long, probability that the diameter is OK is computed here using bayes theorem as:
= Number of rods with diameter OK and too long length / Number of rods with too long rods
= 25 / ( 25 + 2 + 13 )
= 25 / 40
= 0.625
Therefore (iii) is the required probability here.
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