A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability that 5 out of a shipment of 30 will be defective is 0.001617.
<h3>What is Binomial distribution?</h3>
A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
The probability of the bulb being defective is 3%(0.03) and the probability of the bulb not being defective is 97%(0.97).
Now, it is needed to be found that the probability that 5 out of a shipment of 30 will be defective can be written as,
P(x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾
P(x=5) = ³⁰C₅ (0.03)⁵ (0.97)²⁵
P(x=5) = 0.001617
Hence, the probability that 5 out of a shipment of 30 will be defective is 0.001617.
Learn more about Binomial Distribution:
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= 81