I am strugling with the following: The lifetime of a mechanical assembly follows Normal distribution N(30,5). The manufacturer aims to replace all purchased items failing before a guaranteed minimum lifetime of t time-units. Calculate the maximum value of k under the restriction that at most 9% of the purchased products can be replaced. I suppose i have to calculate P(X<k)=9%? and The probability that in 50 independent purchases there will be at least 3 items that will fail before 4 units of time. Do i have to calculate the probability of p=P(X<4), where X follows N(30,5) and then calculate the probability P(Y>=3), where Y follows Bin(50,p)? Thank you in advance
Hi Idk I don't recognise that question from the course notes or IFOA, so please share a reference if you have one. Yes, correct, calculate P(X<k)=9%. and Yes, correct, calculate p first, where p=P(X<4), where X follows N(30,5) and then calculate the probability P(Y>=3), where Y follows Bin(50,p). Andrea
