Question

7. The lifetimes of interactive computer chips produced by a certain semiconductor manufacturer follow Chi-square distribution with mean u=12 years. What is the probability that a batch of 20 chips will contain at least 1 whose lifetimes are longer than 21 years?

Answer 1

Answer:

Given,

Mean = 12

Here mean is n = 12

P($\chi ^{2}_{12}$ > 21) = 1 - P($\chi ^{2}_{12}$ < 21)

= 1 - 0.9666

= 0.0334

P($\chi ^{2}_{12}$ > 21) = 0.0334

Now here we are using Binomial distribution

n = 20

p = 0.0334

q = 1 - p

= 1 - 0.0334

q = 0.9666

Now consider,

P(Y >= 1) = 1 - P(Y < 1)

= 1 - P(Y = 0)

= 1 - 20C0*0.0334^0*0.9666^20

= 1 - 1*1*0.9666^20

= 1 - 0.5069

= 0.4931

Required probability = 0.4931