Historical Airline regestration data showed that the weight

Historical Airline regestration data showed that the weight W of travellers bags is uniformly distributed between 10 and 40 kg (i.e W~ U[10,40], f(W) =1/30 ). The airline company classify a bag with more 30 Kg as heavy.

a) what is the probability that a randomly selected bag is heavy?

b) Determine the probability that at most 3 bags would e checked to identify a heavy bag?

c) determine the probability that exactly 2 out of 10 randomly selected bags would be heavy?

Solution

W is uniform

a) P(W>30) = 10/30 = 0.333

b) P(at most 3 bags) = P(0) +P(1)+P(2)+P(3)

= 0.333+0.333²+0.333³ (as each bag is independent)

c) P(2 out of 10 bags) = 10C2(0.333)²(0.667)⁸