Suppose the phone company decided to add a check digit as the 11th digit in all phone nu...

Suppose the phone company decided to add a check digit as the 11th digit in all phone numbers so that a telephone call would not ring if an error was made when placing the call. For a 10-digit phone number consisting of a 3-digit area code followed by a 7-digit number, suppose the check digit is calculated as follows (the check digit is the last digit in the sum):

a. Calculate the check digit for the phone number (583) 259-3671.

b. Will all single-digit errors be detected? Explain why or why not.

c. Will all adjacent transposition errors be detected? Explain why or why not.