Temperature transducars of a certain type are shipped in batches of 50. A sampla
ID: 3068370 • Letter: T
Question
Temperature transducars of a certain type are shipped in batches of 50. A sampla of 60 batches was selected, and the numher af transducers in ach batch nat confarming to design specificatians was determinnd, resulting in the follawing data: 2 1 2 41 1 3 2 0 5 3 31 32 47 0 2 3 0 4 2 13 1 1 3 4 1 2 3 2 28 441 3 I (a) Determine frequencies and relative frequencies for the observed values ofxnumber of nonconforming transducers in a batch. (Round your relative frequencies to three decimal places.) Relati Frequency b) What proportion of batches in the sample have at most six n g transducers? (Round your answer to three decimal places.) What proportion have fewer than six? (Round your answer to hree dcimal places.) What proportion hve at least six nonconforming units? (Round your answer to three decimal places.)Explanation / Answer
Solution :
From Given information
(a) x Nonconforming Relative
Frequency Frequency
0 6 6/60 = 0.100
1 13 13/60 = 0.217
2 13 13/60 = 0.217
3 14 14/60 = 0.233
4 7 7/60 = 0.117
5 2 2/60 = 0.033
6 2 2/60 = 0.033
7 2 2/60 = 0.033
8 1 1/60 = 0.017
=> x = number of nonconforming transducers in a batch
=> Relative frequency = x/n
(b) => P(x >= 6)
=> P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5) + P(x = 6)
=> 6 + 13 + 13 + 14 + 7 + 2 + 2
=> 57
=> The number of batches with atmost 6 nonconforming trnsducers is = 57
=> The required proportion is = 57/60 = 0.950
=> P(x > 6)
=> P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5)
=> 6 + 13 + 13 + 14 + 7 + 2
=> 55
=> The number of batches with fewer than 6 nonconforming items is = 55
=> The required proportion is = 55/60 = 0.917
=> P(x <= 6)
=> P(x = 6) + P(x = 7) + P(x = 8)
=> 2 + 2 + 1
=> 5
=> The number of batches with at least 6 nonconforming units is = 5
=> The required proportion is = 5/60 = 0.083
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