3 added 1 character in body
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Perl 6, 68 6363 59 bytes

{S:g/./{chrs((768..815). roll(0 max (0,-140+[+]140+sum rand xx 300))~$/,768..815}$//}

Try it online!Try it online!

t̤̣̜̉̌̂̇̍h̢̙̦̩̉ȇ̡̡̢̛̞̠̔̑̃̊̑̓ ̗̩̜̎̒̑i̛̭̤̘̒c̛̤̮̔́̑̃̔̅̐̑̚hǫ̘̣̩̣̙̙̆̎̂̉̋̊̕r̨̦̯̋̀̊̀ ̥̙̉̓̃̇̑p̢̨̛̯̗̥̞̞̘̬̪̗̠̖̅̅̉̃́̀̐̉e̖̋r̒̐m̧̖̪̉̐ẻä̪̞ţ̯̠̦̖̍̍̋̅̊̀̕ḙ̡̡̙̐̓̌̉̌ŝ̢̧̝̃̉̀ ̡̮̘̤̙̤̘̋̃̂̋̊̐̀̏̋̐̐̒ą̛̞̥̦̘̌̊̋̂̂̒̆l̢̛̛̮̘̜̦̝̫̮̪̟̭̖̜̅̑̂̍̑̉ḷ̨̞̜̤̠̣̪̥̋̀̇̊̊̍̈ ̢̢̤̜̬̫̊̇̑̐̇̑̒̕Ḿ̢̭̫̘̟̟̤̮́̃̎Y̧̬̖̜̆̀̍̍̐̒̉̒ ̡̗̔̎̆̆̀́̎F̬̯̯̏Â̡̛̝̭̎̂̉̑C̡̦̄̑̓Ę̛̭̞̤̂̓̔̃̎̓̏ ̛̪̬̯̘́̐̚MÝ̛̝̫̥̖̓̏̑̀ ̘̤̄́̍F̬̯̠̩̞̊̃̓̔̕Ă̙̥̞̤̕C̪̓̆E̡̟̝̭̦̮̎̒̅́ ̭̈̋ḣ̢̛̫̗̩̩̣̭̋̎̐̃̄̈̉̓ ̦̘̖̃̉̔̂̆̃̍̅̕g̡̧̢̜̬̪̞̟̒̇̊́̃̋̚ǭ̫̣̩̙̆̏̏̌̑̀̕d̟̮̠̬̙̗̥̪̭̜̐̑̊̔̕̕ ̨̙̠̟̠̯̆̑̅̒̔ṋ̛̘̜̞̦̈̋̋̍̋̈ơ̡̧̗̟̟̩̙̔̏̀̈̀̇̇̆̎̕ ̨̛̦̎̀̕N̛̄̋Ò̢̡̙̦̓̑̒̂̆́ ̧̗̮̠̗̮̯̆̉̑̅N̛̤̤̒O̧̤̯̯̦̥̒̍̏̃̇̊̕Ő̜̩̙̂̀̎̕Ọ̝̗̆̉Ơ̢̦̫̭̪̐̚̚ ̨̢̞̊̉̑̍̎̆̒N̡̞̭̙̏̏̓̄̚ ̠̖̫̦̗̓̉́s̤̄̋t̨̞̫̣̭̏̔̀ở̜̘̝̉ṗ̧̬̗̥̫̤̗̣̄̋̒̎́̒ ̯́̃̕ṭ̮̖̟̥̗̤́̊̋̇̎ḩ̞̜̗̪̊̂̏e̢̞̬̟̟̠̗̎̌̐̏̔̒ ̥̠̞̉̌́̈́̈̏̍ä̡̨̩̩̯̦̐̂n̢̟̫̖̯̞̗̙̙̊̋̐̍̚*̢̘́̒̉̎̚g̛̗̬̐̂́̇̉̆̀̚l̨̢̦̪̬̤̤̂̀̇̉̂̍̒̚ȩ̧̢̖̘̠̓̐́̈̌s̘̯̘̒̉̆̒̄̈̇̕ ̡̧̛̬̠̣̮̅ă̗̮̖̜̥̟̮̋̅̉̍̅̕r̢̢̢̤̩̙̩̋̑̓̍̆̍̕̚e̡̛̙̗̅̄̄̒́̚ ̡̖̫̞̖̖̟̣̭̅̐̄̑̊̃̉̎ǹ̗̟̤̄ö̪̏̎t̡̛̫̥̗̫̠̜̪̏̒ ̡̡̢̜̮̭̇̒̋̑̏̃̓̕r̡̗̬̯̪̝̮̂̊̒̏̔̉̀̚e̢̧̗̯̞̭̘̝̐̓̈̔̊̋̉å̖̣̔̋l̡̛̛̬̮̟̝̪̯̆̊ ̡̪̩̐̒Z̡̦̗̝̞̜̠̊̇̓̆AḶ̒̇̇̅̓̈̃̂Ğ̮̯̭̮̘̞̙̣̐̐̉̇Ő̡̠̞̄ ̢̟̖̪̋́́̔̚̚Į̪̗̭̖̊Ș̢̬̤̜̥̟̌̅ ̨̢̜̥̪̠̦̦̦̘̟̯̯̋̒̓̍̈̇̕T̢̉̆̌̊̎̈̕Ȍ̧̢̫̬̄̉̀̇̍̍̌̚̕Ņ̥̩̝̟̀̈̀̇̆̏̕y̛̟̫̠̭̫̗̫̮̬̥̥̭̗̓̏̑̋̍̇̐̔̋̐̅ ̝̥̘̫̪̖̫̅̂̌́̎̀̚̚̕Ṭ̌H̦̫̖̟̥̣̔̚̕Ę̢̬̮̩̣̙̇̅ ̨̧̝̭̩̟̈̂̈̃̓̓̚P̩̞̭̠̝̗̂̓̒̋̄Ợ̙̬̜̮̄̑̊̏̒N̘̤̆̏̇Y̨̫̪̜̖̯̒̎̋̌̍̈̄̊ ̧̣̠̣̜̌̄̇̋̄̊̉̏H̛̠̮̣̝̩̖̋̑̍E ̡̢̙̘̥̬̗̯̄̌̔̂̀̆̇̔̑C̪̣̮̋̇̎O̧̨̩̖̠̓̓̉̚̚̕M̛̛̙̘̟̪̙̘̩̝̖̉́̀̂̏̇Ẻ̡̛̛̘̯̜̆̀̓̓̒S


Uses the, ahem, 'binomial approximation' to the normal...

Text from that bobince answer.

Perl 6, 68 63 bytes

{S:g/./{chrs((768..815).roll(0 max -140+[+] rand xx 300))~$/}/}

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t̤̣̜̉̌̂̇̍h̢̙̦̩̉ȇ̡̡̢̛̞̠̔̑̃̊̑̓ ̗̩̜̎̒̑i̛̭̤̘̒c̛̤̮̔́̑̃̔̅̐̑̚hǫ̘̣̩̣̙̙̆̎̂̉̋̊̕r̨̦̯̋̀̊̀ ̥̙̉̓̃̇̑p̢̨̛̯̗̥̞̞̘̬̪̗̠̖̅̅̉̃́̀̐̉e̖̋r̒̐m̧̖̪̉̐ẻä̪̞ţ̯̠̦̖̍̍̋̅̊̀̕ḙ̡̡̙̐̓̌̉̌ŝ̢̧̝̃̉̀ ̡̮̘̤̙̤̘̋̃̂̋̊̐̀̏̋̐̐̒ą̛̞̥̦̘̌̊̋̂̂̒̆l̢̛̛̮̘̜̦̝̫̮̪̟̭̖̜̅̑̂̍̑̉ḷ̨̞̜̤̠̣̪̥̋̀̇̊̊̍̈ ̢̢̤̜̬̫̊̇̑̐̇̑̒̕Ḿ̢̭̫̘̟̟̤̮́̃̎Y̧̬̖̜̆̀̍̍̐̒̉̒ ̡̗̔̎̆̆̀́̎F̬̯̯̏Â̡̛̝̭̎̂̉̑C̡̦̄̑̓Ę̛̭̞̤̂̓̔̃̎̓̏ ̛̪̬̯̘́̐̚MÝ̛̝̫̥̖̓̏̑̀ ̘̤̄́̍F̬̯̠̩̞̊̃̓̔̕Ă̙̥̞̤̕C̪̓̆E̡̟̝̭̦̮̎̒̅́ ̭̈̋ḣ̢̛̫̗̩̩̣̭̋̎̐̃̄̈̉̓ ̦̘̖̃̉̔̂̆̃̍̅̕g̡̧̢̜̬̪̞̟̒̇̊́̃̋̚ǭ̫̣̩̙̆̏̏̌̑̀̕d̟̮̠̬̙̗̥̪̭̜̐̑̊̔̕̕ ̨̙̠̟̠̯̆̑̅̒̔ṋ̛̘̜̞̦̈̋̋̍̋̈ơ̡̧̗̟̟̩̙̔̏̀̈̀̇̇̆̎̕ ̨̛̦̎̀̕N̛̄̋Ò̢̡̙̦̓̑̒̂̆́ ̧̗̮̠̗̮̯̆̉̑̅N̛̤̤̒O̧̤̯̯̦̥̒̍̏̃̇̊̕Ő̜̩̙̂̀̎̕Ọ̝̗̆̉Ơ̢̦̫̭̪̐̚̚ ̨̢̞̊̉̑̍̎̆̒N̡̞̭̙̏̏̓̄̚ ̠̖̫̦̗̓̉́s̤̄̋t̨̞̫̣̭̏̔̀ở̜̘̝̉ṗ̧̬̗̥̫̤̗̣̄̋̒̎́̒ ̯́̃̕ṭ̮̖̟̥̗̤́̊̋̇̎ḩ̞̜̗̪̊̂̏e̢̞̬̟̟̠̗̎̌̐̏̔̒ ̥̠̞̉̌́̈́̈̏̍ä̡̨̩̩̯̦̐̂n̢̟̫̖̯̞̗̙̙̊̋̐̍̚*̢̘́̒̉̎̚g̛̗̬̐̂́̇̉̆̀̚l̨̢̦̪̬̤̤̂̀̇̉̂̍̒̚ȩ̧̢̖̘̠̓̐́̈̌s̘̯̘̒̉̆̒̄̈̇̕ ̡̧̛̬̠̣̮̅ă̗̮̖̜̥̟̮̋̅̉̍̅̕r̢̢̢̤̩̙̩̋̑̓̍̆̍̕̚e̡̛̙̗̅̄̄̒́̚ ̡̖̫̞̖̖̟̣̭̅̐̄̑̊̃̉̎ǹ̗̟̤̄ö̪̏̎t̡̛̫̥̗̫̠̜̪̏̒ ̡̡̢̜̮̭̇̒̋̑̏̃̓̕r̡̗̬̯̪̝̮̂̊̒̏̔̉̀̚e̢̧̗̯̞̭̘̝̐̓̈̔̊̋̉å̖̣̔̋l̡̛̛̬̮̟̝̪̯̆̊ ̡̪̩̐̒Z̡̦̗̝̞̜̠̊̇̓̆AḶ̒̇̇̅̓̈̃̂Ğ̮̯̭̮̘̞̙̣̐̐̉̇Ő̡̠̞̄ ̢̟̖̪̋́́̔̚̚Į̪̗̭̖̊Ș̢̬̤̜̥̟̌̅ ̨̢̜̥̪̠̦̦̦̘̟̯̯̋̒̓̍̈̇̕T̢̉̆̌̊̎̈̕Ȍ̧̢̫̬̄̉̀̇̍̍̌̚̕Ņ̥̩̝̟̀̈̀̇̆̏̕y̛̟̫̠̭̫̗̫̮̬̥̥̭̗̓̏̑̋̍̇̐̔̋̐̅ ̝̥̘̫̪̖̫̅̂̌́̎̀̚̚̕Ṭ̌H̦̫̖̟̥̣̔̚̕Ę̢̬̮̩̣̙̇̅ ̨̧̝̭̩̟̈̂̈̃̓̓̚P̩̞̭̠̝̗̂̓̒̋̄Ợ̙̬̜̮̄̑̊̏̒N̘̤̆̏̇Y̨̫̪̜̖̯̒̎̋̌̍̈̄̊ ̧̣̠̣̜̌̄̇̋̄̊̉̏H̛̠̮̣̝̩̖̋̑̍E ̡̢̙̘̥̬̗̯̄̌̔̂̀̆̇̔̑C̪̣̮̋̇̎O̧̨̩̖̠̓̓̉̚̚̕M̛̛̙̘̟̪̙̘̩̝̖̉́̀̂̏̇Ẻ̡̛̛̘̯̜̆̀̓̓̒S


Uses the, ahem, 'binomial approximation' to the normal...

Text from that bobince answer.

Perl 6, 68 63 59 bytes

{S:g/./{chrs roll max(0,-140+sum rand xx 300),768..815}$//}

Try it online!

t̤̣̜̉̌̂̇̍h̢̙̦̩̉ȇ̡̡̢̛̞̠̔̑̃̊̑̓ ̗̩̜̎̒̑i̛̭̤̘̒c̛̤̮̔́̑̃̔̅̐̑̚hǫ̘̣̩̣̙̙̆̎̂̉̋̊̕r̨̦̯̋̀̊̀ ̥̙̉̓̃̇̑p̢̨̛̯̗̥̞̞̘̬̪̗̠̖̅̅̉̃́̀̐̉e̖̋r̒̐m̧̖̪̉̐ẻä̪̞ţ̯̠̦̖̍̍̋̅̊̀̕ḙ̡̡̙̐̓̌̉̌ŝ̢̧̝̃̉̀ ̡̮̘̤̙̤̘̋̃̂̋̊̐̀̏̋̐̐̒ą̛̞̥̦̘̌̊̋̂̂̒̆l̢̛̛̮̘̜̦̝̫̮̪̟̭̖̜̅̑̂̍̑̉ḷ̨̞̜̤̠̣̪̥̋̀̇̊̊̍̈ ̢̢̤̜̬̫̊̇̑̐̇̑̒̕Ḿ̢̭̫̘̟̟̤̮́̃̎Y̧̬̖̜̆̀̍̍̐̒̉̒ ̡̗̔̎̆̆̀́̎F̬̯̯̏Â̡̛̝̭̎̂̉̑C̡̦̄̑̓Ę̛̭̞̤̂̓̔̃̎̓̏ ̛̪̬̯̘́̐̚MÝ̛̝̫̥̖̓̏̑̀ ̘̤̄́̍F̬̯̠̩̞̊̃̓̔̕Ă̙̥̞̤̕C̪̓̆E̡̟̝̭̦̮̎̒̅́ ̭̈̋ḣ̢̛̫̗̩̩̣̭̋̎̐̃̄̈̉̓ ̦̘̖̃̉̔̂̆̃̍̅̕g̡̧̢̜̬̪̞̟̒̇̊́̃̋̚ǭ̫̣̩̙̆̏̏̌̑̀̕d̟̮̠̬̙̗̥̪̭̜̐̑̊̔̕̕ ̨̙̠̟̠̯̆̑̅̒̔ṋ̛̘̜̞̦̈̋̋̍̋̈ơ̡̧̗̟̟̩̙̔̏̀̈̀̇̇̆̎̕ ̨̛̦̎̀̕N̛̄̋Ò̢̡̙̦̓̑̒̂̆́ ̧̗̮̠̗̮̯̆̉̑̅N̛̤̤̒O̧̤̯̯̦̥̒̍̏̃̇̊̕Ő̜̩̙̂̀̎̕Ọ̝̗̆̉Ơ̢̦̫̭̪̐̚̚ ̨̢̞̊̉̑̍̎̆̒N̡̞̭̙̏̏̓̄̚ ̠̖̫̦̗̓̉́s̤̄̋t̨̞̫̣̭̏̔̀ở̜̘̝̉ṗ̧̬̗̥̫̤̗̣̄̋̒̎́̒ ̯́̃̕ṭ̮̖̟̥̗̤́̊̋̇̎ḩ̞̜̗̪̊̂̏e̢̞̬̟̟̠̗̎̌̐̏̔̒ ̥̠̞̉̌́̈́̈̏̍ä̡̨̩̩̯̦̐̂n̢̟̫̖̯̞̗̙̙̊̋̐̍̚*̢̘́̒̉̎̚g̛̗̬̐̂́̇̉̆̀̚l̨̢̦̪̬̤̤̂̀̇̉̂̍̒̚ȩ̧̢̖̘̠̓̐́̈̌s̘̯̘̒̉̆̒̄̈̇̕ ̡̧̛̬̠̣̮̅ă̗̮̖̜̥̟̮̋̅̉̍̅̕r̢̢̢̤̩̙̩̋̑̓̍̆̍̕̚e̡̛̙̗̅̄̄̒́̚ ̡̖̫̞̖̖̟̣̭̅̐̄̑̊̃̉̎ǹ̗̟̤̄ö̪̏̎t̡̛̫̥̗̫̠̜̪̏̒ ̡̡̢̜̮̭̇̒̋̑̏̃̓̕r̡̗̬̯̪̝̮̂̊̒̏̔̉̀̚e̢̧̗̯̞̭̘̝̐̓̈̔̊̋̉å̖̣̔̋l̡̛̛̬̮̟̝̪̯̆̊ ̡̪̩̐̒Z̡̦̗̝̞̜̠̊̇̓̆AḶ̒̇̇̅̓̈̃̂Ğ̮̯̭̮̘̞̙̣̐̐̉̇Ő̡̠̞̄ ̢̟̖̪̋́́̔̚̚Į̪̗̭̖̊Ș̢̬̤̜̥̟̌̅ ̨̢̜̥̪̠̦̦̦̘̟̯̯̋̒̓̍̈̇̕T̢̉̆̌̊̎̈̕Ȍ̧̢̫̬̄̉̀̇̍̍̌̚̕Ņ̥̩̝̟̀̈̀̇̆̏̕y̛̟̫̠̭̫̗̫̮̬̥̥̭̗̓̏̑̋̍̇̐̔̋̐̅ ̝̥̘̫̪̖̫̅̂̌́̎̀̚̚̕Ṭ̌H̦̫̖̟̥̣̔̚̕Ę̢̬̮̩̣̙̇̅ ̨̧̝̭̩̟̈̂̈̃̓̓̚P̩̞̭̠̝̗̂̓̒̋̄Ợ̙̬̜̮̄̑̊̏̒N̘̤̆̏̇Y̨̫̪̜̖̯̒̎̋̌̍̈̄̊ ̧̣̠̣̜̌̄̇̋̄̊̉̏H̛̠̮̣̝̩̖̋̑̍E ̡̢̙̘̥̬̗̯̄̌̔̂̀̆̇̔̑C̪̣̮̋̇̎O̧̨̩̖̠̓̓̉̚̚̕M̛̛̙̘̟̪̙̘̩̝̖̉́̀̂̏̇Ẻ̡̛̛̘̯̜̆̀̓̓̒S


Uses the, ahem, 'binomial approximation' to the normal...

Text from that bobince answer.

2 added 5 characters in body
source | link

Perl 6, 6868 63 bytes

{S:g/./{chrs(|(768..815).roll(0 max -140+[+] rand xx 300),$/.ord)~$/}/}

Try it online!Try it online!

t̤̣̜̉̌̂̇̍h̢̙̦̩̉ȇ̡̡̢̛̞̠̔̑̃̊̑̓ ̗̩̜̎̒̑i̛̭̤̘̒c̛̤̮̔́̑̃̔̅̐̑̚hǫ̘̣̩̣̙̙̆̎̂̉̋̊̕r̨̦̯̋̀̊̀ ̥̙̉̓̃̇̑p̢̨̛̯̗̥̞̞̘̬̪̗̠̖̅̅̉̃́̀̐̉e̖̋r̒̐m̧̖̪̉̐ẻä̪̞ţ̯̠̦̖̍̍̋̅̊̀̕ḙ̡̡̙̐̓̌̉̌ŝ̢̧̝̃̉̀ ̡̮̘̤̙̤̘̋̃̂̋̊̐̀̏̋̐̐̒ą̛̞̥̦̘̌̊̋̂̂̒̆l̢̛̛̮̘̜̦̝̫̮̪̟̭̖̜̅̑̂̍̑̉ḷ̨̞̜̤̠̣̪̥̋̀̇̊̊̍̈ ̢̢̤̜̬̫̊̇̑̐̇̑̒̕Ḿ̢̭̫̘̟̟̤̮́̃̎Y̧̬̖̜̆̀̍̍̐̒̉̒ ̡̗̔̎̆̆̀́̎F̬̯̯̏Â̡̛̝̭̎̂̉̑C̡̦̄̑̓Ę̛̭̞̤̂̓̔̃̎̓̏ ̛̪̬̯̘́̐̚MÝ̛̝̫̥̖̓̏̑̀ ̘̤̄́̍F̬̯̠̩̞̊̃̓̔̕Ă̙̥̞̤̕C̪̓̆E̡̟̝̭̦̮̎̒̅́ ̭̈̋ḣ̢̛̫̗̩̩̣̭̋̎̐̃̄̈̉̓ ̦̘̖̃̉̔̂̆̃̍̅̕g̡̧̢̜̬̪̞̟̒̇̊́̃̋̚ǭ̫̣̩̙̆̏̏̌̑̀̕d̟̮̠̬̙̗̥̪̭̜̐̑̊̔̕̕ ̨̙̠̟̠̯̆̑̅̒̔ṋ̛̘̜̞̦̈̋̋̍̋̈ơ̡̧̗̟̟̩̙̔̏̀̈̀̇̇̆̎̕ ̨̛̦̎̀̕N̛̄̋Ò̢̡̙̦̓̑̒̂̆́ ̧̗̮̠̗̮̯̆̉̑̅N̛̤̤̒O̧̤̯̯̦̥̒̍̏̃̇̊̕Ő̜̩̙̂̀̎̕Ọ̝̗̆̉Ơ̢̦̫̭̪̐̚̚ ̨̢̞̊̉̑̍̎̆̒N̡̞̭̙̏̏̓̄̚ ̠̖̫̦̗̓̉́s̤̄̋t̨̞̫̣̭̏̔̀ở̜̘̝̉ṗ̧̬̗̥̫̤̗̣̄̋̒̎́̒ ̯́̃̕ṭ̮̖̟̥̗̤́̊̋̇̎ḩ̞̜̗̪̊̂̏e̢̞̬̟̟̠̗̎̌̐̏̔̒ ̥̠̞̉̌́̈́̈̏̍ä̡̨̩̩̯̦̐̂n̢̟̫̖̯̞̗̙̙̊̋̐̍̚*̢̘́̒̉̎̚g̛̗̬̐̂́̇̉̆̀̚l̨̢̦̪̬̤̤̂̀̇̉̂̍̒̚ȩ̧̢̖̘̠̓̐́̈̌s̘̯̘̒̉̆̒̄̈̇̕ ̡̧̛̬̠̣̮̅ă̗̮̖̜̥̟̮̋̅̉̍̅̕r̢̢̢̤̩̙̩̋̑̓̍̆̍̕̚e̡̛̙̗̅̄̄̒́̚ ̡̖̫̞̖̖̟̣̭̅̐̄̑̊̃̉̎ǹ̗̟̤̄ö̪̏̎t̡̛̫̥̗̫̠̜̪̏̒ ̡̡̢̜̮̭̇̒̋̑̏̃̓̕r̡̗̬̯̪̝̮̂̊̒̏̔̉̀̚e̢̧̗̯̞̭̘̝̐̓̈̔̊̋̉å̖̣̔̋l̡̛̛̬̮̟̝̪̯̆̊ ̡̪̩̐̒Z̡̦̗̝̞̜̠̊̇̓̆AḶ̒̇̇̅̓̈̃̂Ğ̮̯̭̮̘̞̙̣̐̐̉̇Ő̡̠̞̄ ̢̟̖̪̋́́̔̚̚Į̪̗̭̖̊Ș̢̬̤̜̥̟̌̅ ̨̢̜̥̪̠̦̦̦̘̟̯̯̋̒̓̍̈̇̕T̢̉̆̌̊̎̈̕Ȍ̧̢̫̬̄̉̀̇̍̍̌̚̕Ņ̥̩̝̟̀̈̀̇̆̏̕y̛̟̫̠̭̫̗̫̮̬̥̥̭̗̓̏̑̋̍̇̐̔̋̐̅ ̝̥̘̫̪̖̫̅̂̌́̎̀̚̚̕Ṭ̌H̦̫̖̟̥̣̔̚̕Ę̢̬̮̩̣̙̇̅ ̨̧̝̭̩̟̈̂̈̃̓̓̚P̩̞̭̠̝̗̂̓̒̋̄Ợ̙̬̜̮̄̑̊̏̒N̘̤̆̏̇Y̨̫̪̜̖̯̒̎̋̌̍̈̄̊ ̧̣̠̣̜̌̄̇̋̄̊̉̏H̛̠̮̣̝̩̖̋̑̍E ̡̢̙̘̥̬̗̯̄̌̔̂̀̆̇̔̑C̪̣̮̋̇̎O̧̨̩̖̠̓̓̉̚̚̕M̛̛̙̘̟̪̙̘̩̝̖̉́̀̂̏̇Ẻ̡̛̛̘̯̜̆̀̓̓̒S


Uses the, ahem, 'binomial approximation' to the normal...

Text from that bobince answer.

Perl 6, 68 bytes

{S:g/./{chrs(|(768..815).roll(0 max -140+[+] rand xx 300),$/.ord)}/}

Try it online!

t̤̣̜̉̌̂̇̍h̢̙̦̩̉ȇ̡̡̢̛̞̠̔̑̃̊̑̓ ̗̩̜̎̒̑i̛̭̤̘̒c̛̤̮̔́̑̃̔̅̐̑̚hǫ̘̣̩̣̙̙̆̎̂̉̋̊̕r̨̦̯̋̀̊̀ ̥̙̉̓̃̇̑p̢̨̛̯̗̥̞̞̘̬̪̗̠̖̅̅̉̃́̀̐̉e̖̋r̒̐m̧̖̪̉̐ẻä̪̞ţ̯̠̦̖̍̍̋̅̊̀̕ḙ̡̡̙̐̓̌̉̌ŝ̢̧̝̃̉̀ ̡̮̘̤̙̤̘̋̃̂̋̊̐̀̏̋̐̐̒ą̛̞̥̦̘̌̊̋̂̂̒̆l̢̛̛̮̘̜̦̝̫̮̪̟̭̖̜̅̑̂̍̑̉ḷ̨̞̜̤̠̣̪̥̋̀̇̊̊̍̈ ̢̢̤̜̬̫̊̇̑̐̇̑̒̕Ḿ̢̭̫̘̟̟̤̮́̃̎Y̧̬̖̜̆̀̍̍̐̒̉̒ ̡̗̔̎̆̆̀́̎F̬̯̯̏Â̡̛̝̭̎̂̉̑C̡̦̄̑̓Ę̛̭̞̤̂̓̔̃̎̓̏ ̛̪̬̯̘́̐̚MÝ̛̝̫̥̖̓̏̑̀ ̘̤̄́̍F̬̯̠̩̞̊̃̓̔̕Ă̙̥̞̤̕C̪̓̆E̡̟̝̭̦̮̎̒̅́ ̭̈̋ḣ̢̛̫̗̩̩̣̭̋̎̐̃̄̈̉̓ ̦̘̖̃̉̔̂̆̃̍̅̕g̡̧̢̜̬̪̞̟̒̇̊́̃̋̚ǭ̫̣̩̙̆̏̏̌̑̀̕d̟̮̠̬̙̗̥̪̭̜̐̑̊̔̕̕ ̨̙̠̟̠̯̆̑̅̒̔ṋ̛̘̜̞̦̈̋̋̍̋̈ơ̡̧̗̟̟̩̙̔̏̀̈̀̇̇̆̎̕ ̨̛̦̎̀̕N̛̄̋Ò̢̡̙̦̓̑̒̂̆́ ̧̗̮̠̗̮̯̆̉̑̅N̛̤̤̒O̧̤̯̯̦̥̒̍̏̃̇̊̕Ő̜̩̙̂̀̎̕Ọ̝̗̆̉Ơ̢̦̫̭̪̐̚̚ ̨̢̞̊̉̑̍̎̆̒N̡̞̭̙̏̏̓̄̚ ̠̖̫̦̗̓̉́s̤̄̋t̨̞̫̣̭̏̔̀ở̜̘̝̉ṗ̧̬̗̥̫̤̗̣̄̋̒̎́̒ ̯́̃̕ṭ̮̖̟̥̗̤́̊̋̇̎ḩ̞̜̗̪̊̂̏e̢̞̬̟̟̠̗̎̌̐̏̔̒ ̥̠̞̉̌́̈́̈̏̍ä̡̨̩̩̯̦̐̂n̢̟̫̖̯̞̗̙̙̊̋̐̍̚*̢̘́̒̉̎̚g̛̗̬̐̂́̇̉̆̀̚l̨̢̦̪̬̤̤̂̀̇̉̂̍̒̚ȩ̧̢̖̘̠̓̐́̈̌s̘̯̘̒̉̆̒̄̈̇̕ ̡̧̛̬̠̣̮̅ă̗̮̖̜̥̟̮̋̅̉̍̅̕r̢̢̢̤̩̙̩̋̑̓̍̆̍̕̚e̡̛̙̗̅̄̄̒́̚ ̡̖̫̞̖̖̟̣̭̅̐̄̑̊̃̉̎ǹ̗̟̤̄ö̪̏̎t̡̛̫̥̗̫̠̜̪̏̒ ̡̡̢̜̮̭̇̒̋̑̏̃̓̕r̡̗̬̯̪̝̮̂̊̒̏̔̉̀̚e̢̧̗̯̞̭̘̝̐̓̈̔̊̋̉å̖̣̔̋l̡̛̛̬̮̟̝̪̯̆̊ ̡̪̩̐̒Z̡̦̗̝̞̜̠̊̇̓̆AḶ̒̇̇̅̓̈̃̂Ğ̮̯̭̮̘̞̙̣̐̐̉̇Ő̡̠̞̄ ̢̟̖̪̋́́̔̚̚Į̪̗̭̖̊Ș̢̬̤̜̥̟̌̅ ̨̢̜̥̪̠̦̦̦̘̟̯̯̋̒̓̍̈̇̕T̢̉̆̌̊̎̈̕Ȍ̧̢̫̬̄̉̀̇̍̍̌̚̕Ņ̥̩̝̟̀̈̀̇̆̏̕y̛̟̫̠̭̫̗̫̮̬̥̥̭̗̓̏̑̋̍̇̐̔̋̐̅ ̝̥̘̫̪̖̫̅̂̌́̎̀̚̚̕Ṭ̌H̦̫̖̟̥̣̔̚̕Ę̢̬̮̩̣̙̇̅ ̨̧̝̭̩̟̈̂̈̃̓̓̚P̩̞̭̠̝̗̂̓̒̋̄Ợ̙̬̜̮̄̑̊̏̒N̘̤̆̏̇Y̨̫̪̜̖̯̒̎̋̌̍̈̄̊ ̧̣̠̣̜̌̄̇̋̄̊̉̏H̛̠̮̣̝̩̖̋̑̍E ̡̢̙̘̥̬̗̯̄̌̔̂̀̆̇̔̑C̪̣̮̋̇̎O̧̨̩̖̠̓̓̉̚̚̕M̛̛̙̘̟̪̙̘̩̝̖̉́̀̂̏̇Ẻ̡̛̛̘̯̜̆̀̓̓̒S


Uses the, ahem, 'binomial approximation' to the normal...

Text from that bobince answer.

Perl 6, 68 63 bytes

{S:g/./{chrs((768..815).roll(0 max -140+[+] rand xx 300))~$/}/}

Try it online!

t̤̣̜̉̌̂̇̍h̢̙̦̩̉ȇ̡̡̢̛̞̠̔̑̃̊̑̓ ̗̩̜̎̒̑i̛̭̤̘̒c̛̤̮̔́̑̃̔̅̐̑̚hǫ̘̣̩̣̙̙̆̎̂̉̋̊̕r̨̦̯̋̀̊̀ ̥̙̉̓̃̇̑p̢̨̛̯̗̥̞̞̘̬̪̗̠̖̅̅̉̃́̀̐̉e̖̋r̒̐m̧̖̪̉̐ẻä̪̞ţ̯̠̦̖̍̍̋̅̊̀̕ḙ̡̡̙̐̓̌̉̌ŝ̢̧̝̃̉̀ ̡̮̘̤̙̤̘̋̃̂̋̊̐̀̏̋̐̐̒ą̛̞̥̦̘̌̊̋̂̂̒̆l̢̛̛̮̘̜̦̝̫̮̪̟̭̖̜̅̑̂̍̑̉ḷ̨̞̜̤̠̣̪̥̋̀̇̊̊̍̈ ̢̢̤̜̬̫̊̇̑̐̇̑̒̕Ḿ̢̭̫̘̟̟̤̮́̃̎Y̧̬̖̜̆̀̍̍̐̒̉̒ ̡̗̔̎̆̆̀́̎F̬̯̯̏Â̡̛̝̭̎̂̉̑C̡̦̄̑̓Ę̛̭̞̤̂̓̔̃̎̓̏ ̛̪̬̯̘́̐̚MÝ̛̝̫̥̖̓̏̑̀ ̘̤̄́̍F̬̯̠̩̞̊̃̓̔̕Ă̙̥̞̤̕C̪̓̆E̡̟̝̭̦̮̎̒̅́ ̭̈̋ḣ̢̛̫̗̩̩̣̭̋̎̐̃̄̈̉̓ ̦̘̖̃̉̔̂̆̃̍̅̕g̡̧̢̜̬̪̞̟̒̇̊́̃̋̚ǭ̫̣̩̙̆̏̏̌̑̀̕d̟̮̠̬̙̗̥̪̭̜̐̑̊̔̕̕ ̨̙̠̟̠̯̆̑̅̒̔ṋ̛̘̜̞̦̈̋̋̍̋̈ơ̡̧̗̟̟̩̙̔̏̀̈̀̇̇̆̎̕ ̨̛̦̎̀̕N̛̄̋Ò̢̡̙̦̓̑̒̂̆́ ̧̗̮̠̗̮̯̆̉̑̅N̛̤̤̒O̧̤̯̯̦̥̒̍̏̃̇̊̕Ő̜̩̙̂̀̎̕Ọ̝̗̆̉Ơ̢̦̫̭̪̐̚̚ ̨̢̞̊̉̑̍̎̆̒N̡̞̭̙̏̏̓̄̚ ̠̖̫̦̗̓̉́s̤̄̋t̨̞̫̣̭̏̔̀ở̜̘̝̉ṗ̧̬̗̥̫̤̗̣̄̋̒̎́̒ ̯́̃̕ṭ̮̖̟̥̗̤́̊̋̇̎ḩ̞̜̗̪̊̂̏e̢̞̬̟̟̠̗̎̌̐̏̔̒ ̥̠̞̉̌́̈́̈̏̍ä̡̨̩̩̯̦̐̂n̢̟̫̖̯̞̗̙̙̊̋̐̍̚*̢̘́̒̉̎̚g̛̗̬̐̂́̇̉̆̀̚l̨̢̦̪̬̤̤̂̀̇̉̂̍̒̚ȩ̧̢̖̘̠̓̐́̈̌s̘̯̘̒̉̆̒̄̈̇̕ ̡̧̛̬̠̣̮̅ă̗̮̖̜̥̟̮̋̅̉̍̅̕r̢̢̢̤̩̙̩̋̑̓̍̆̍̕̚e̡̛̙̗̅̄̄̒́̚ ̡̖̫̞̖̖̟̣̭̅̐̄̑̊̃̉̎ǹ̗̟̤̄ö̪̏̎t̡̛̫̥̗̫̠̜̪̏̒ ̡̡̢̜̮̭̇̒̋̑̏̃̓̕r̡̗̬̯̪̝̮̂̊̒̏̔̉̀̚e̢̧̗̯̞̭̘̝̐̓̈̔̊̋̉å̖̣̔̋l̡̛̛̬̮̟̝̪̯̆̊ ̡̪̩̐̒Z̡̦̗̝̞̜̠̊̇̓̆AḶ̒̇̇̅̓̈̃̂Ğ̮̯̭̮̘̞̙̣̐̐̉̇Ő̡̠̞̄ ̢̟̖̪̋́́̔̚̚Į̪̗̭̖̊Ș̢̬̤̜̥̟̌̅ ̨̢̜̥̪̠̦̦̦̘̟̯̯̋̒̓̍̈̇̕T̢̉̆̌̊̎̈̕Ȍ̧̢̫̬̄̉̀̇̍̍̌̚̕Ņ̥̩̝̟̀̈̀̇̆̏̕y̛̟̫̠̭̫̗̫̮̬̥̥̭̗̓̏̑̋̍̇̐̔̋̐̅ ̝̥̘̫̪̖̫̅̂̌́̎̀̚̚̕Ṭ̌H̦̫̖̟̥̣̔̚̕Ę̢̬̮̩̣̙̇̅ ̨̧̝̭̩̟̈̂̈̃̓̓̚P̩̞̭̠̝̗̂̓̒̋̄Ợ̙̬̜̮̄̑̊̏̒N̘̤̆̏̇Y̨̫̪̜̖̯̒̎̋̌̍̈̄̊ ̧̣̠̣̜̌̄̇̋̄̊̉̏H̛̠̮̣̝̩̖̋̑̍E ̡̢̙̘̥̬̗̯̄̌̔̂̀̆̇̔̑C̪̣̮̋̇̎O̧̨̩̖̠̓̓̉̚̚̕M̛̛̙̘̟̪̙̘̩̝̖̉́̀̂̏̇Ẻ̡̛̛̘̯̜̆̀̓̓̒S


Uses the, ahem, 'binomial approximation' to the normal...

Text from that bobince answer.

1
source | link

Perl 6, 68 bytes

{S:g/./{chrs(|(768..815).roll(0 max -140+[+] rand xx 300),$/.ord)}/}

Try it online!

t̤̣̜̉̌̂̇̍h̢̙̦̩̉ȇ̡̡̢̛̞̠̔̑̃̊̑̓ ̗̩̜̎̒̑i̛̭̤̘̒c̛̤̮̔́̑̃̔̅̐̑̚hǫ̘̣̩̣̙̙̆̎̂̉̋̊̕r̨̦̯̋̀̊̀ ̥̙̉̓̃̇̑p̢̨̛̯̗̥̞̞̘̬̪̗̠̖̅̅̉̃́̀̐̉e̖̋r̒̐m̧̖̪̉̐ẻä̪̞ţ̯̠̦̖̍̍̋̅̊̀̕ḙ̡̡̙̐̓̌̉̌ŝ̢̧̝̃̉̀ ̡̮̘̤̙̤̘̋̃̂̋̊̐̀̏̋̐̐̒ą̛̞̥̦̘̌̊̋̂̂̒̆l̢̛̛̮̘̜̦̝̫̮̪̟̭̖̜̅̑̂̍̑̉ḷ̨̞̜̤̠̣̪̥̋̀̇̊̊̍̈ ̢̢̤̜̬̫̊̇̑̐̇̑̒̕Ḿ̢̭̫̘̟̟̤̮́̃̎Y̧̬̖̜̆̀̍̍̐̒̉̒ ̡̗̔̎̆̆̀́̎F̬̯̯̏Â̡̛̝̭̎̂̉̑C̡̦̄̑̓Ę̛̭̞̤̂̓̔̃̎̓̏ ̛̪̬̯̘́̐̚MÝ̛̝̫̥̖̓̏̑̀ ̘̤̄́̍F̬̯̠̩̞̊̃̓̔̕Ă̙̥̞̤̕C̪̓̆E̡̟̝̭̦̮̎̒̅́ ̭̈̋ḣ̢̛̫̗̩̩̣̭̋̎̐̃̄̈̉̓ ̦̘̖̃̉̔̂̆̃̍̅̕g̡̧̢̜̬̪̞̟̒̇̊́̃̋̚ǭ̫̣̩̙̆̏̏̌̑̀̕d̟̮̠̬̙̗̥̪̭̜̐̑̊̔̕̕ ̨̙̠̟̠̯̆̑̅̒̔ṋ̛̘̜̞̦̈̋̋̍̋̈ơ̡̧̗̟̟̩̙̔̏̀̈̀̇̇̆̎̕ ̨̛̦̎̀̕N̛̄̋Ò̢̡̙̦̓̑̒̂̆́ ̧̗̮̠̗̮̯̆̉̑̅N̛̤̤̒O̧̤̯̯̦̥̒̍̏̃̇̊̕Ő̜̩̙̂̀̎̕Ọ̝̗̆̉Ơ̢̦̫̭̪̐̚̚ ̨̢̞̊̉̑̍̎̆̒N̡̞̭̙̏̏̓̄̚ ̠̖̫̦̗̓̉́s̤̄̋t̨̞̫̣̭̏̔̀ở̜̘̝̉ṗ̧̬̗̥̫̤̗̣̄̋̒̎́̒ ̯́̃̕ṭ̮̖̟̥̗̤́̊̋̇̎ḩ̞̜̗̪̊̂̏e̢̞̬̟̟̠̗̎̌̐̏̔̒ ̥̠̞̉̌́̈́̈̏̍ä̡̨̩̩̯̦̐̂n̢̟̫̖̯̞̗̙̙̊̋̐̍̚*̢̘́̒̉̎̚g̛̗̬̐̂́̇̉̆̀̚l̨̢̦̪̬̤̤̂̀̇̉̂̍̒̚ȩ̧̢̖̘̠̓̐́̈̌s̘̯̘̒̉̆̒̄̈̇̕ ̡̧̛̬̠̣̮̅ă̗̮̖̜̥̟̮̋̅̉̍̅̕r̢̢̢̤̩̙̩̋̑̓̍̆̍̕̚e̡̛̙̗̅̄̄̒́̚ ̡̖̫̞̖̖̟̣̭̅̐̄̑̊̃̉̎ǹ̗̟̤̄ö̪̏̎t̡̛̫̥̗̫̠̜̪̏̒ ̡̡̢̜̮̭̇̒̋̑̏̃̓̕r̡̗̬̯̪̝̮̂̊̒̏̔̉̀̚e̢̧̗̯̞̭̘̝̐̓̈̔̊̋̉å̖̣̔̋l̡̛̛̬̮̟̝̪̯̆̊ ̡̪̩̐̒Z̡̦̗̝̞̜̠̊̇̓̆AḶ̒̇̇̅̓̈̃̂Ğ̮̯̭̮̘̞̙̣̐̐̉̇Ő̡̠̞̄ ̢̟̖̪̋́́̔̚̚Į̪̗̭̖̊Ș̢̬̤̜̥̟̌̅ ̨̢̜̥̪̠̦̦̦̘̟̯̯̋̒̓̍̈̇̕T̢̉̆̌̊̎̈̕Ȍ̧̢̫̬̄̉̀̇̍̍̌̚̕Ņ̥̩̝̟̀̈̀̇̆̏̕y̛̟̫̠̭̫̗̫̮̬̥̥̭̗̓̏̑̋̍̇̐̔̋̐̅ ̝̥̘̫̪̖̫̅̂̌́̎̀̚̚̕Ṭ̌H̦̫̖̟̥̣̔̚̕Ę̢̬̮̩̣̙̇̅ ̨̧̝̭̩̟̈̂̈̃̓̓̚P̩̞̭̠̝̗̂̓̒̋̄Ợ̙̬̜̮̄̑̊̏̒N̘̤̆̏̇Y̨̫̪̜̖̯̒̎̋̌̍̈̄̊ ̧̣̠̣̜̌̄̇̋̄̊̉̏H̛̠̮̣̝̩̖̋̑̍E ̡̢̙̘̥̬̗̯̄̌̔̂̀̆̇̔̑C̪̣̮̋̇̎O̧̨̩̖̠̓̓̉̚̚̕M̛̛̙̘̟̪̙̘̩̝̖̉́̀̂̏̇Ẻ̡̛̛̘̯̜̆̀̓̓̒S


Uses the, ahem, 'binomial approximation' to the normal...

Text from that bobince answer.