statistics math

Question

a study was conducted of pleas by 3200 criminals. Among those criminals 2960 pled guilty and 1332 of them were sentenced to prison. among remaining criminals who pled not guilty 195 were sent to prison.

what percentage of criminals pled not guilty?

what percentage of the criminals were sent to prison

what percentage of the criminals who pled guilty were sent to prison

what percentage of the criminals who pled not guilty were sent to prison

if 88% of these criminals had no previous criminal record what number of them did

Answer 1

Hi Isabel,

You need to break this problem down into component parts. It can be overwhelming at first, but it's solvable if you just go piece by piece.

Part 1: what percentage pled not guilty?

You were given that there were 3200 criminals total and 2960 pled guilty. Assuming no one pled nolo contendre:

3200-2960=240 not guilty pleas

To compute percentage:

240/3200=0.075

Multiply by 100:

7.5% pled not guilty

Part 2: What percentage were sent to prison?

Again, assuming no one pled nolo contendre, you were given that 1332 of those who pled guilty and 195 who pled not guilty were sent to prison. Recall that we have 3200 total criminals. So:

(1332+195)/3200=0.477

Multiply by 100:

47.7% of all criminals in sample were sent to prison

Part 3: What percentage of those who pled guilty were sent to prison?

We know that 2960 pled guilty and 1332 of those criminals were sent to prison, so:

1332/2960=0.45

Multiply by 100:

45% of criminals who pled guilty were sent to prison.

Part 4: What percentage of those who pled guilty were sent to prison?

Recall from part 1 that we had 240 not guilty pleas. You were given that 195 went to prison, so:

195/240=0.8125

Multiply by 100:

81.25% of criminals who pled not guilty were sent to prison

Part 5: If 88% of criminals had no previous criminal record, what number of them did.

We know right out of the gate that 12% of the criminals had previous records, since that is a yes/no question. We also know that there were 3200 total criminals. To compute this number, convert 12% to a decimal and multiply by the total:

12%=0.12

0.12*3200=384

384 criminals had previous records

Good luck and I hope this helps.

Answer 2