Light bulbs manufactured at a certain factory have a 3% probability of being defective. what is the probability that 5 out of a

Question

GalinKa [24]

2 years ago

9

Light bulbs manufactured at a certain factory have a 3% probability of being defective. what is the probability that 5 out of a

shipment of 30 will be defective? a. 0.25 b. 0.0016 c. 0.0035 d. 0.167

Mathematics

1 answer:

lbvjy [14] · Answer 1 · 2023-06-25T22:50:39+03:00

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.