​Z-Score

The LRA Crisis Tracker

For over two decades, the Lord's Resistance Army (LRA) has been abducting children and inciting violence against civilians in remote areas of central Africa. In 2010, the non-profit Invisible Children put a plan in place to build a sustainable early warning radio network so civilians could broadcast for help if their homes were attacked by LRA forces.
All data received from this radio network is routed through the LRA Crisis Tracker. Check it out below.

✔ Discussion 1
​Think about the planning needed to implement the early warning radio network system in the isolation of central Africa. What resources would an electrical engineer need to build and operate the radio towers? 

HF Radio

Radio waves in the High Frequency (HF) band are ideal for long distances because they can be reflected by a layer of Earth's atmosphere. However, this means that the distances the HF radio waves can travel are extremely variable based on the season or whether it is day or night.
​The LRA Crisis Tracker operates with HF radio towers. Knowing the dependable radio distance range could be vital information when broadcasting a message.

​✔ Figure 1
When communicating from base to base on a HF radio network, the mean dependable radio distance range is 30 miles with a standard deviation of 1 mile. Draw the normal curve for this distribution.

​Calculating the Z-Score

✔ Notes 1

The normal distribution defines segments of the curve based on how many standard deviations a value is from the mean. However, a value won't always be 1 or 2 standard deviations away from the mean - it could be 1.5, or 2.7 standard deviations away from the mean.

The z-score of a value gives how many standard deviations that value is from the mean.
Once you have a z-score, you can use a z-score table to determine the percentage of values below the given value.

Try an Example!

✔ ​Calculation 1
Using the normal distribution from Figure 1, find the z-score for 31.5 miles.
Then, use the z-score table to determine what percentage of values are below 31.5 miles. So, 93.32% of dependable radio distance ranges are below the value of 31.5 miles. 

✔ Calculation 2
When communicating from base to vehicle on a HF radio network, the mean dependable radio distance range is 20 miles with a standard deviation of 1.5 miles.
  • What percent of values are below 19 miles?
  • What percent of values are above 19 miles?
  • What percent of values are below 22 miles?
  • What percent of values are above 22 miles?

✔ Calculation 3
When communicating from vehicle to vehicle on a HF radio network, the mean dependable radio distance range is 15 miles with a standard deviation of 2.2 miles.
  • What percent of values are above 11 miles?
  • What percent of values are above 13 miles?
  • What percent of values are in between 11 and 13 miles?

✔ Discussion 2 
​Percentage of values under the normal curve can also be represented as the probability of a value being chosen. Why might this information be important to an electrical engineer working on an early warning radio network?

NOAA Weather Radio All Hazards

NOAA Weather Radio All Hazards (NWR) is a nationwide network of radio stations broadcasting continuous weather information directly from the nearest National Weather Service office. NWR broadcasts official Weather Service warnings, watches, forecasts and other hazard information 24 hours a day, 7 days a week.