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.

b.What is the probability that exactly one of the LED light bulbs is ​defective?

The probability that exactly one of the LED light bulbs is defective is

_____

​(Typean integer or a decimal. Round to four decimal places as​needed.)

Answer 1

The Given problem is solved using Binomial distribution:

Binomial Distribution

If 'X' is the random variable representing the number of successes, the probability of getting ‘r’ successes and ‘n-r’ failures, in 'n' trails, ‘p’ probability of success ‘q’=(1-p) is given by the probability function

Failure rate for LED light bulbs that the company manufactures is 14 ​%.

Probability that a randomly selected LED light bulb is defective: p = 14/100 = 0.14

Probability that a randomly selected LED light bulb is not defective: q = 1-p = 1-0.14 = 0.86

Number of  LED light bulbs selected in the sample n = 10

Let X : Number of LED light bulbs in the sample are defective

Applying above Binomial distribution as defined above

X follows a Binomial distribution with n= 10 , p=0.14 , q=0.86

Probability function of X : Probability that 'r' LED light bulbs are ​defective

Probability that exactly one of the LED light bulbs is ​defective = P(X=1)

Probability that exactly one of the LED light bulbs is ​defective = 0.3603