u/Lich-Su answered a very similar question to this here some time ago.
In the United States, about 1.8 million men reached draft age each year in the 1960s, and roughly a third (600,000) were disqualified as unsuitable for military service, half of these for physical reasons and the other half for mental or educational reasons.
As the United States’ involvement in the Vietnam War escalated, in August 1966, Secretary of Defense Robert McNamara instituted a controversial plan. Men who scored in the lower percentiles of the Armed Forces Qualification Test (AFQT) or were otherwise mentally or physically unsuitable for general service under the present requirements would be able to serve in the military in larger numbers through reduction of requirements and promotion of voluntary enlistments. The goal was 40,000 men for the rest of 1966 and then 100,000 additional men per year, to relieve pressure on Selective Service local boards. The experiment was often later derisively referred to as “McNamara’s Morons,” or the “Moron Corps.”
The main focus of “Project 100,000” was enlisting those men who scored below the 30th percentile of the AFQT, with additional requirements depending upon the branch of service as scores decreased. Men who scored below the 10th percentile were still excepted. The regular military physical standards were not changed, but waivers were granted for a list of mild or easily correctable medical conditions;
Under minimum weight by not more than 10%
Over maximum weight by not more than 20%
Undescended testicle and inguinal hernia, same side
Orthopedic fixture at site of old fracture
Simple goiter
External otitis
Hyperdactylia (hands and feet)
Deviated nasal septum
Pilonidal cyst or sinus cyst
Hemorrhoids
Undescended testicle, unilateral
Varicocele
Hydrocele
Hernia of the abdominal cavity
Each fiscal year, per a quota system, a maximum of one percent of the “Project 100,000” in the Army and Marine Corps, and two percent in the Navy and Air Force, were permitted to enter with these medical waivers. About 80% of the waivers granted were for underweight or overweight cases. During basic training, the men were expected to meet the same performance standards as normal soldiers, but additional help was offered. A larger percentage of “Project 100,000” men were non-white (38%) compared to the control group (10%), and on average, they had completed one grade level less of schooling. More were from the southern United States. A larger percentage of the “New Standards Men” (another official name) were also assigned to combat-related military jobs.
The project ended in December 1971 when the Department of Defense prohibited the use of mental capacity quotas for accepting men into the military. 354,000 men entered military service under “Project 100,000” between October 1966 and December 1971, with a peak of 103,000 during fiscal year 1969. 54 percent of men voluntarily enlisted, while 46 percent were drafted. 67 percent of the men went to the Army.
In the movie, Forrest Gump is stated to have an IQ of 75, in roughly the 13th percentile nationwide. As u/Lich-Su noted in their answer, the military converted projected AFQT scores to IQ scores and vice versa, and Forrest would have been on the lower end of Category IV, with just a high enough score to qualify for service mentally without further intervention. This is exclusive of his ability to follow military procedures and directions from his commanding officers. Given his physical prowess as also depicted in the film, he would have qualified easily in that regard.
Conversion of Mental Category Scores from AFQT to IQ Scores
| Mental [AFQT] Categories | Percentiles | Stanford-Binet IQ | Wechsler IQ |
|---|---|---|---|
| I | 93-99 | 124 and above | 122 and above |
| II | 65-92 | 108-123 | 106-121 |
| III | 31-64 | 92-107 | 93-105 |
| IV | 10-30 | 72-91 | 81-92 |
| V | 1-9 | 71 and below | 80 and below |
Sources:
Previous answer of u/Lich-Su
Project 100,000: New Standards Program (RAND publication)
Relation Between AFQT and IQ (RAND publication)