Defects in yarn manufactured by a local mill can be approximated by a distribution with a mean of 1.2 defects for every 6 metres of length. If lengths of 6 metres are to be inspected, find the probability of less than 2 defects.
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Answer:
0.793
Step-by-step explanation:
Mean = np
=> 1.2 = 6 * p
=> p = 0.2
Probability of Defect = 0.2
1- p = 1 - 0.2 = 0.8
Standard Deviation = √np(1-p)
= √6 * 0.2 * 0.8
= 0.98
Z = (value - Mean)/SD
Z = ( 2 - 1.2)/0.98
=> Z = 0.8/0.98
=> Z = 0.8163
using Z table
the probability of less than 2 defects 0.793
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