Suppose the air traffic controller randomly samples 100 days and recordsthe number of delayed flights on each day. Find the probability that the totalnumber of delayed flights over the 100 days is less than 250. Assume that the numberof delayed flights on each day is independent and has a probability distribution givenby the table above.

At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.08 and the probability that the flight will be delayed is 0.09. The probability that it will not rain and the flight will leave on time is 0.87. What is the probability that the flight would be delayed when it is not raining? Round your answer to the nearest thousandth.

A company delivers packages, and the delivery time (𝑇)(T) for a package follows an exponential distribution with a mean of 30 minutes. Suppose the company delivers 𝑛n packages in a day. What is the minimum number of packages 𝑛n required to ensure that the probability that the average delivery time (𝑇‾)( T ) for the day lies between 28 and 32 minutes is at least 0.95? Use CLT to approximate.

The number of accidents (𝐴) at an intersection is counted for a 12-hour period. The number of accidents follows a Poisson distribution with a parameter value of 2.Calculate the probability that there will be no accidents in a 1-hour period.

The last 1500 Air America flights 315 have been delayed. What is the probability that a flight with this airline will not be delayed?

A visitor is coming for a seminar in UQ. The probability that he comes by train, car and flight is respectively 0.5, 0.3 and 0.2. And the probability of delay by these three means of transport is respectively 0.1, 0.3 and 0.4. If the visitor is late, what is the probability that he came by train? (The result retains four decimals)