Question

A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company
manufactures is 14%. Suppose a random sample of 10 LED light bulbs is selected. Complete parts (a) through (d) below.
a. What is the probability that none of the LED light bulbs are defective?
The probability that none of the LED light bulbs are defective is
(Type an integer or a decint. Round to four decimal places as needed.)

Answer 1

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability that none of the LED light bulbs are defective is 0.2213.

What is Binomial distribution?

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.

Given the probability of a bulb being a failure is 14%, therefore, the probability of bulb passing the quality check is 86%.

Let the probability of success be defined as 0.14 for binomial distribution, and the probability for failure be 0.86. Therefore, The probability that none of the LED light bulbs are defective is

P(x=0) = ¹⁰C₀ (0.14)⁰ (0.86)¹⁰ = 0.2213

Hence, The probability that none of the LED light bulbs are defective is 0.2213.

Learn more about Binomial Distribution:

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