Question

A civil engineer is collecting data on a certain road. She needs to have data on 25 trucks, and 10 percent of the vehicles on that road are trucks. State the famous parametric family that is relevant here, and find the probability that she will need to wait for more than 200 vehicles to pass before she gets the needed data.

Answer 1

The probability of getting a vehicle as a truck is given as 10% = 0.1. Therefore p = 0.1

For collecting the data on 25 trucks, the total number of vehicles to wait for is modelled as a negative bionomial distribution with r = 25 and p = 0.1

Now the probability to wait for more than 200 vehicles to pass before she gets the needed data is computed here as:

= Probability of getting less than equal to 24 trucks in the first 200 vehicles.

The number of trucks in the first 200 vehicles could be modelled here as:

This is approximated as a normal distribution as:

The probability required here is:

Applying the continuity correction, we get here:

P(X < 24.5 )

Converting this to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.8556 is the required probability here.