Question

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.​

Answer 1

in yarn manufacturing, with a mean of 1.2 defects for every 6 metres of length, the probability of less than 2 defects. in 6m length = 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