Question

Flight Arrivals. Listed below are the arrival delay times (min) of randomly selected American Airlines flights that departed from JFK in New York bound for LAX in Los Angeles. Negative values correspond to flights that arrived early and ahead of the scheduled arrival time. Use these values for Exercises 1–4.

-30 -23 14 -21 -32 11 -23 28 103 -19 -5 -46

Range Rule of Thumb Use the results from Exercise 1 “Statistics” with the range rule of thumb to find arrival times separating those that are significantly low and those that are significantly high. Is the arrival delay time of 103 min significantly high?

Short answer

Values that are equal to or greater than 76.1 minutes are significantly high.

Values that are equal to or less than -83.3 minutes are significantly low.

Values that lie between -83.3 minutes and 76.1 minutes are not significant.

103 minutes is a significantly high value as it is greater than 76.1 minutes.

Step-by-step solution

Given information

A sample of arrival delay times (in minutes) is given for a set of American Airlines flights from New York to LA.

Range rule of thumb

The range rule of thumb for identifying significant values has the following three features:

Values that are equal to or greater than 2 standard deviations above the mean are significantly high.

Values that are equal to or less than 2 standard deviations below the mean are significantly low.

Values that lie within 2 standard deviations of the mean are not significant.

Calculation of the limits and checking the significance of a sample value

Refer to Exercise 1CRE, where the sample mean value of the arrival delay times is equal to -3.6 minutes, and the standard deviation of the arrival delay times is equal to 39.9 minutes.

The limit that separates the significantly high values is computed below.

.$$\begin{gathered} \overline{x}+2s=\left(-3.6\right)+2\left(39.9\right) \\ =76.2 \end{gathered}$$

Thus, values that are equal to or greater than 76.1 minutes are significantly high.

The limit that separates the significantly low values is computed below.

$$\begin{gathered} \overline{x}-2s=\left(-3.6\right)-2\left(39.9\right) \\ =-83.4 \end{gathered}$$

Thus, values that are equal to or less than -83.4 minutes are significantly low.

Values that lie between -83.4 minutes and 76.2 minutes are not significant.

The value equal to 103 minutes is significantly high as it is greater than 76.2 minutes.