Coox and Naisawald's 1954 study Survey of Allied Tank Casualties in World War II gives several statistics that attempt to determine this.

A study of 800 U.S., British, and Canadian tank casualties in Western Europe, the Mediterranean Theater, and North Africa disclosed that the average range at which tanks were immobilized by gunfire was under 800 yards. A sample of 100 tank casualties in North Africa showed an average range of 900 yards; 60 tank casualties in Sicily and Italy--350 yards; 650 tank casualties in Western Europe--over 800 yards. These figures are explicable by the fact that in the western desert of North Africa, where the terrain favored ranges to the limits of visibility, tank fighting often resembled naval battles which boiled down to "slug fests" where light vessels (=light tanks and armored cars) were involved. A figure of 900 yards represents the averaging out of engagements at 1500 to 2000 yards as well as those at hub-to-hub range, e.g., Knightsbridge; Rommel's brilliant tank traps allowed his antitank guns to effect kills at short range. Martel has explained the reasons for the Germans' electing to fight armor at longer ranges in the desert as follows:

The German armored forces often attacked British unarmored troops if they found them insufficiently protected by artillery and antitank guns, but they always avoided closing with our tanks in a running fight. When meeting British tanks in strength they preferred to take up a position which was well protected by artillery fire and with antitank guns on the flanks, and used the superior gunfire from stationary tanks to shoot at the British tanks at long range.

It should be stressed that the data on range are almost always derived from "subjective" estimates given in after-action reports or "third-hand" summaries. The only exception is a portion of the British ETO sample, wherein operations research teams from the 21st Army Group actually examined tanks immobilized after the Rhine crossing. The over-all average of 800 yards range is also probably higher than the actual figure, if it were known, for a much larger sample, inasmuch as a further 75 tank casualties to gunfire were listed only as "close," "fairly close," "point-blank," "various," etc.

TABLE VIII

AVERAGE RANGES AT WHICH TANKS WERE IMMOBILIZED

(Sampling) [gunfire only]

Category	Sample	Range (yds)
US: ETO-First Army	330	796.4
ETO-Third, Seventh, Ninth Armies	119	713.7
ITALY	3	758.9
US: Total	452	774.4
UK: ETO	190	886.3
ITALY	51	348.1
SICILY	6	300.0
AFRICA	96	890.1
UK: Total	343	797.1
CANADA: ETO	5	432.0
ETO: US, UK, CANADA	644	804.8
All Theaters: US, UK, CANADA	800	782.0

Hardison's Data on World War II Tank Engagements: Involving the U.S. Third and Fourth Armored Divisions also gives a figure that is about 800 to 900 yards on average.

TABLE V

SUMMARY OF RANGES AT WHICH ALLIED AND ENEMY TANKS WERE DESTROYED IN VARIOUS AREAS OF NORTHWEST EUROPE

Area	Number of Allied Casualties	Average Allied Casualty Range in Yards	Number of Enemy Casualties	Average Enemy Casualty Range in Yards
Vicinity Stolberg	26	476
Roer to Rhine	37	959	6	733
Belgian Bulge	60	1000	9	833
Vicinity Arracourt	20	1260	74	936
Sarre	37	1116	35	831
Relief of Bastogne	19	731	16	915
Totals	199	946	140	893

It was shown in the referenced report that the distribution of combat ranges is approximately represented by a Pearson III distribution function of the form:

F(R) = e^-X (X + 1)

X = 2R sqrt R

R = range, Rbar = average range,

F(R) = fraction of ranges greater than R.

Unfortunately, I do not have any average numbers on the range, but I can talk about the general tank engagements at Prokhorovka. At the battle of Prokhorovka the fighting was unusually close and there is a very logical explanation for this. The best German tanks at the battlefield was the Tiger, and it was very well armored and had a powerful gun. Opposing this the Red Army fielded mostly T-34s. The T-34s had 45mm of angled armor at the front, but this was no match for the Tigers 88mm. In fact, the 88mm was so powerful that it could penetrate the armor of a T-34 at over 2000 m, maybe up to 3500 meters. On the contrary the thick armor of the Tiger made it almost impregnable on everything but close combat. So much that Rotmistrov, the commander of the Red Army forces at Prokhorovka, said that “successful struggle with [Tigers and Ferdinands] is possible only in circumstances of close-in-combat [and by exploiting] the T-34s greater maneuverability and by flanking fire against the [weaker] side armour of the German machines” (Clark, p.364). As seen Rotmistrov was aware of the Tigers and Ferdinands superiority and therefor adjusted his tactics to compensate. This lead to the 5th Guards Tank Army (Rotmistrovs formation) charging the German positions seeking to get as close as possible. A important flaw in Rotmistrovs planning was that he had massively overestimated the amount of Tigers available to the Germans, and would probably be better of being a bit more careful. (Clark, p. 364-365). Nevertheless, the Russians carried on which lead to a fierce close-range engagement between the two sides. Rudolf von Ribbentrop, the son of the German foreign minister and a commander of a Panzer IV company describes the battle:

“We halted on a slope and opened fire, hitting several of the enemy. A number of Russian tanks were left burning. For a good gunner 800 metres was the ideal range. And we waited to see if further enemy tanks were going to appear, I looked around[…]. What I saw made me speechless. From beyond the shallow rise about 150-200 metres in front of me appeared fifteen, then thirty, then forty tanks. Finally there were to many to count. The T-34s were rolling forward toward us at high speed, carrying mounted infantry…soon the first round was on its way and, with its impact, the T-34 began to burn. It was only fifty to seventy metres from us. At the same instant the tank next to me took a direct hit and went up in flames… His neighbour to the right was also hit and soon he was also in flames. The avalanche of enemy tanks rolled straight toward us: Tank after tank! Wave after wave! It was simply an unimaginable assembly, and it was moving at very high speed.

Similarly, the Russian T-34 commander Vasili Bryukhov writes:

"The distance between the tanks was below 100 metres – it was impossible to maneuvre a tank[…] it was not a battle, it was a slaughterhouse of tanks. We crawled back and forth and fired. Everything was burning. An indescribable stench hung in the air over the battlefield.”

Sources: Clark, L. (2012). Kursk. London: Headline Review.