Question

Normality Assessment A random sample consists of 48 times (min) required for American Airlines flights to taxi out for takeoff. All of the flights are American Airlines flights from New York (JFK) to Los Angeles and they all occurred in January of a recent year. The 48 taxi-out times are depicted in the histogram and normal quantile plot shown below. Based on those graphs, does it appear that the taxi-out times are from a population having a normal distribution? Give an explanation for the distribution shown. Do the taxi-out times appear to satisfy the requirements necessary for construction of a confidence interval estimate of the standard deviation of the population of all such times?

Short answer

It does not appear that the taxi-out times are from a population that is normally distributed.

The distribution depicted in the graphs appears to be skewed towards the right or positively skewed.

The taxi-out times do not satisfy the requirement necessary for the construction of a confidence interval estimate of the population standard deviation

Step-by-step solution

Given information

A sample of times required for 48 American Airlines flights to taxi out for takeoff is considered.

A histogram and a normal quantile plot are constructed for the sample values.

Shape of the histogram 

If a histogram depicting sample values is bell-shaped, the sample can be considered to be from a normally distributed population.

The histogram shows atail on the right side.That is, it appears that the distribution is skewed towards the right or positively skewed.

Since the histogram is far from being bell-shaped, the population of times required to taxi out for takeoff is not normally distributed. Rather, the distribution is skewed.

Pattern of points on the normal quantile plot

In the given normal quantile plot, the points do not appear to form a straight line pattern.

Most of the points are clustered towards the left of the plot, and only a few points occur on the right side. This means that the distribution is positively skewed.

Since the points on the plot do not close to a straight line,the population of times required to taxi out for takeoff is not normally distributed. Instead, the distribution is skewed.

Requirement needed for constructing the confidence interval estimate of the standard deviation

One of the requirements that must be fulfilled is that the sample should be strictly from a normally distributed population, irrespective of the sample size.

Here, although the sample size is greater than 30, the sample does not appear to be taken from a normally distributed population.

Thus, the taxi-out times do not satisfy the requirement needed for constructing the confidence interval estimate of the standard deviation.