The probability of accepting this shipment is 98%.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here, we have
Almost all such shipments will be accepted because the probability of having a sample with more than 3 defective batteries is very low.
The shipment will be accepted if at most 3 batteries don't meet specifications.
This can be modeled as a binomial distribution, where the sample size is n=55 and the probability of not meeting the specifications of any battery is p=0.02.
The shipment will be accepted if D ≤ 3.
The probability of this event is:
P( D ≤ 3) = P(D=0) + P(D=1) + P(D=2) + P(D=3)
P(D=X) = n!/(x!(n-x)!) pˣ(1-p)ⁿ⁻ˣ
P(D=0) = 55!/(0!(55-0)!) 0.02⁰(1-0.02)⁵⁵⁻⁰ = 1× 1 × 0.32 = 0.32
P(D=1) = 55!/(1!(55-1)!) 0.02¹(1-0.02)⁵⁴ = 54 × 0.02 × 0.33= 0.35
P(D=2) = 55!/(2!(55-2)!) 0.02²(1-0.02)⁵³ = 55 ×27 × 0.0004 × 0.34= 0.20
P(D=3) = 55!/(3!(55-3)!) 0.02³(1-0.02)⁵² = 25740× 0.0000008 × 0.35= 0.07
Then,
P( D ≤ 3) = P(D=0) + P(D=1) + P(D=2) + P(D=3)
P( D ≤ 3) = 0.32 + 0.35 + 0.20 + 0.07
P( D ≤ 3) = 0.98
Hence, the probability of accepting this shipment is 98%.
To learn more about the probability from the given link
brainly.com/question/24756209
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