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2 answers:
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Answer:
(a) The probability that at least 13 of the next 15 motherboards pass inspection is 0.6042.
(b) On average, 1.18 motherboards should be inspected until a motherboard that passes inspection is found.
Step-by-step explanation:
Let <em>X</em> = number of motherboards that pass the inspection.
The probability that a motherboards pass the inspection is P (X) = <em>p</em> = 0.85.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.
The probability mass function of <em>X</em> is,
(a)
Compute the probability that at least 13 of the next 15 motherboards pass inspection as follows:
P (X ≥ 13) = P (X= 13) + P (X = 14) + P (x = 15)
Thus, the probability that at least 13 of the next 15 motherboards pass inspection is 0.6042.
(b)
Computed the expected number of motherboards should be inspected until a motherboard that passes inspection is found as follows:
Thus, on average, 1.18 motherboards should be inspected until a motherboard that passes inspection is found.