Answer to Question #122219 in Statistics and Probability for ali

Question

Super bikes arrive in a 12 lot showroom. Inspections are carried out on six out of every 12. For
one lot, it is known 2 out of 12 do not meet the safety standards prescribed. What is the
probability that at least 2 out of the 6 that were tested from that lot will not meet safety
standards?

Answer 1

Poisson distribution

P(x=X)=(λ^xe^-λ)/x!

P(x≥2)=P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)=(2²e^-2)/2!+(2³e^-2)/3!+(2⁴e^-2)/4!+(2⁵e^-2)/5!+(2⁶e^-2)/6!=0.27+0.18+0.09+0.036+0.012=0.588