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 7%. 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?

b. What is the probability that exactly 1 of the LED light bulbs is defective?

c. What is the probability that 3 or fewer of the LED light bulbs are defective?

d. What is the probability that 4 or more of the LED light bulbs are defective?

Explanation / Answer

Here we will use binomial distribution

p =0.07 n =10 P(X=x)=ncx*px* (1-p)n-x.

1. P(x=0)=10c0*0.070(1-0.07)10=0.484

2. P(x=1)=10c1*0.071*(1-0.07)9=0.364

3. P(x<=3)=0.996 using online calculator

4. P(x>=4)=0.0036 using online calculator

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