A manufacturing company regularly conducts quality control checks at specified p

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 6%.

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 decimal. Round to four decimal places as needed.)

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

(Type an integer or a decimal. Round to four decimal places as needed.)

c. What is the probability that two or fewer of the LED light bulbs are defective?

The probability that two or fewer of the LED light bulbs are defective is

(Type an integer or a decimal. Round to four decimal places as needed.)

d. What is the probability that three or more of the LED light bulbs are defective?

The probability that three or more of the LED light bulbs are defective is

(Type an integer or a decimal. Round to four decimal places as needed.)

Explanation / Answer

Ans:

Binomial distribution:

p=0.06

p=1-0.06=0.94

a)P(r=0)=6C0*0.060*0.946=0.946=0.6899

b)P(r=1)=6C1*0.061*0.945=0.2642

c)P(r<=2)=6C0*0.060*0.946+6C1*0.061*0.945+6C2*0.062*0.942=0.6899+0.2642+0.0422=0.9962

d)P(r>=3)=1-P(r<=2)=1-0.9941=0.0038

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