The probability that a machine will produce all bolts in a production run within specification is 0-998. A sample of 8 machines is taken at random. Calculate the probability that (i) all 8 machines (ii) 7 or 8 machines (iii) at least 6 machines will produce all bolts within specification
Answers
Given : The probability that a machine will produce all bolts in a production run within specification is 0.998
A sample of 8 machines is taken at random.
To Find : Calculate the probability that (i) all 8 machines (ii) 7 or 8 machines (iii) at least 6 machines will produce all bolts within specification
Solution:
Probability that machine produce bolt in specification p = 0.998
Probability that machine does not produce bolt in specification = 1 -0.998
=> q = 0.002
A sample of 8 machines is taken at random.
=> n = 8
P(x) = ⁿCₓpˣqⁿ⁻ˣ
probability that (i) all 8 machines will produce all bolts in a production run within specification
= ⁸C₈(0.998)⁸(0.002)⁸⁻⁸
= (0.998)⁸
(ii) 7 or 8 machines
= ⁸C₈(0.998)⁸(0.002)⁸⁻⁸ +⁸C₇(0.998)⁷(0.002)⁸⁻⁷
= (0.998)⁸ + 8(0.998)⁷(0.002)
= (0.998)⁷( 0.998 + 0.016)
= (0.998)⁷ 1.014
(iii) at least 6 machines will produce all bolts within specification
= ⁸C₈(0.998)⁸(0.002)⁸⁻⁸ +⁸C₇(0.998)⁷(0.002)⁸⁻⁷ + ⁸C₆(0.998)⁶(0.002)⁸⁻⁶
= (0.998)⁸ + 8(0.998)⁷(0.002) + 28(0.998)⁶(0.002)²
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Answer:
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Step-by-step explanation: