Question

a rewiw of anairline s operations revealed that historicall the airline had an average of 6.43 mishandled bags per 1,000 passengers. a mishandled bag is luggage that was not send together with the passenger s plane it was either lost or arrived late

a) what is the chance that for the next 2,000 passengers the airline will have more than 11 mishandled bags?

the chance that for the 2000 pazsengers the airline will have more than 11 misshandle bags is?

b) after a consulting company evaluate the airline s operations the airline overhauled its bag monitoring computer system as a result thr number of mishandled bags per 1,000 passengers decresed by % 30 given that new compute system what is the probability that for the next 3.000 passengers the air line will have fewer that 10 mishandle bags ?

given the new computer system the probability that for the next 3,000 passengers the airline will have fewer that 10 mishandled bag is ?

Answer 1

a.

Probability of having a mishandled bag = 6.43/1000 = 0.00643

Here, we can use Binomial approximation to Normal distribution with parameters :

Probability that for the next 2000 passengers, the airline will have more than 11 mishandled bags = P(X>11)

We use Excel function "NORMSDIST()" as :

Hence,

Probability that for the next 2000 passengers, the airline will have more than 11 mishandled bags = 0.697

b.

Since, the Number of mishandled bags reduced by 30%

So, number of mishandled bags = 6.43*(1-0.30) = 4.49

Hence,

New Probability of having a mishandled bag = 4.45/1000 = 0.00449

Here, we can use Binomial approximation to Normal distribution with parameters :

Probability that for the next 3000 passengers, the airline will have fewer than 10 mishandled bags = P(X<10)

We use Excel function "NORMSDIST()" as :

Hence,

Probability that for the next 3000 passengers, the airline will have fewer than 10 mishandled bags = 0.249