A manufacturing company regularly conducts quality control checks at specifed pe

Question

A manufacturing company regularly conducts quality control checks at specifed periods on the products it manufactu selected Complete parts (a) through (d) below a. What is the probability that none of the LED light buibs are defective? The probability that none of the LED light bulibs are defective is res. Historically ny manufactures is 16% Suppose a random sample of 10 LED light bulbs 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)

Explanation / Answer

Ans:

Use binomial distribution with n=10,p=0.16

P(x=r)=10Cr*0.16r*(1-0.16)10-r

a)P(none)=P(x=0)=(1-0.16)^10=0.1749

b)P(exactly one)=P(x=1)=10C1*0.161*(1-0.16)9=0.3331

c)P(x<=2)=P(x=0)+P(x=1)+P(x=2)

=0.1749+0.3331+0.2856

=0.7936

d)P(x>=3)=1-P(x<=2)=1-0.7936=0.2064

x p(x) 0 0.1749 1 0.3331 2 0.2856 3 0.1450 4 0.0483 5 0.0111 6 0.0018 7 0.0002 8 0.0000 9 0.0000 10 0.0000

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