Approximately how wide is Australia from its easternmost point to its westernmost?

According to wiki.answers.com:
from the most eastern point of Australia (Cape Byron, NSW) to the most western point (Steep Point) is a distance of almost 4000km or 2485 miles.

According to these sites, Cape Byron in NSW to Steep Point in WA is estimated to be a distance of 4000-4467 km (2485-2776 mi). The Australian government site considers it to be approximately 4000 km.

http://australia.gov.au/about-australia/our-country
https://www.answers.com/Q/What_is_the_width_of_Australia_from_east_to_west

On google maps, clicking on Cape Byron NSW in the east and Steep Point WA in the west, gives a great circle distance of 3,987 km (2,477miles).

https://www.google.com/maps/@-28.6379712,153.6364856,15.03z
https://www.google.com/maps/@-26.1475574,113.1574474,13.01z

This site maybe more accurate. Using the actual latitude/longitude co-ordinates, the great circle distance is 3994km (2481 miles):
East: latitude, longitude : -28.63597, 153.63860
West: latitude, longitude : -26.154882, 113.159492
https://www.gpsvisualizer.com/calculators