Question

Please show ALL of your work!

Manufacturers need to determine that each medical linear accelerator works within proper parameters before shipping to hospitals. An individual machine is known to have a probability of failure during initial testing of 0.10. Eight (8) accelerators are tested. (a) What is the probability that at most two (2) fail? (b) What is the probability that none fail?

Answer 1

By using the binomial distribution

n =8

P(fail) = p=0.1

a)

At most two fail is

P(X<=2) = p(x=0)+P(x=1)+P(x=2)

$P(X\leq 2)=\binom{8}{0}(0.10)^0(0.90)^8&plus;\binom{8}{1}(0.10)^1(0.90)^7&plus;\binom{8}{2}(0.10)^2(0.90)^6\\ =0.4305&plus;0.3826&plus;0.1488\\$

P(X<=2) = 0.9619​​​​​​​

b)

None fail means x . =0

$P(X=0)=\binom{8}{0}(0.10)^0(0.90)^8 =\boldsymbol{0.4305}$​​​​​​​