Question

For air travelers, one of the biggest complaints involves the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights.

Answer 1

ANSWER:

According to the "Central Limit Theorem", for large sample size, the sampling distribution of mean always follows normal distribution regardless of the distribution of the given variable.

i.e If X follows any distribution with mean and variance , then

Now since here waiting time is known to have a skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes.

i.e. and   =64

Hence the distribution of mean waiting time will be:

  

i.e.   

Hence mean waiting time will be normally distributed with mean 10 and standard deviation 0.64.