A study was conducted of pleas made by 1,035 criminals. Among those criminals, 959 pled guilty, and 396 of them were sentenced to prison. Among the 76 other criminals, who pled not guilty, 52 were sei prison. Complete (a) through (d). a. What percentage of the criminals pled guilty? $$ 92.7 \% $$ (Round to the nearest tenth as needed.) b. What percentage of the criminals were sent to prison? $$ \% $$ (Round to the nearest tenth as needed.)

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Let's solve the problem step by step.

### Given Data:
- Total criminals: $$ N = 1,035 $$
- Criminals who pled guilty: $$ G = 959 $$
- Criminals sentenced to prison who pled guilty: $$ P_G = 396 $$
- Criminals who pled not guilty: $$ N_G = 76 $$ (which is $$ N - G $$)
- Criminals sentenced to prison who pled not guilty: $$ P_N = 52 $$

### Part (a): Percentage of criminals who pled guilty
To find the percentage of criminals who pled guilty, we use the formula:

$$
\text{Percentage of guilty pleas} = \left( \frac{G}{N} \right) \times 100
$$

Substituting the known values:

$$
\text{Percentage of guilty pleas} = \left( \frac{959}{1035} \right) \times 100
$$

Now, let's calculate this value.

### Part (b): Percentage of criminals sentenced to prison
To find the total number of criminals sentenced to prison, we add the number of guilty and not guilty criminals sentenced to prison:

$$
P = P_G + P_N = 396 + 52
$$

Now, we can find the percentage of criminals sentenced to prison using the formula:

$$
\text{Percentage sentenced to prison} = \left( \frac{P}{N} \right) \times 100
$$

Substituting the values:

$$
\text{Percentage sentenced to prison} = \left( \frac{P}{1035} \right) \times 100
$$

Now, let's perform the calculations for both parts (a) and (b).
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{959}{1035}\times 100$$
- step1: Reduce the numbers:
  $$\frac{959}{207}\times 20$$
- step2: Multiply:
  $$\frac{959\times 20}{207}$$
- step3: Multiply:
  $$\frac{19180}{207}$$
Calculate or simplify the expression $$ (396 + 52)/1035*100 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(396+52\right)}{1035}\times 100$$
- step1: Remove the parentheses:
  $$\frac{396+52}{1035}\times 100$$
- step2: Add the numbers:
  $$\frac{448}{1035}\times 100$$
- step3: Reduce the numbers:
  $$\frac{448}{207}\times 20$$
- step4: Multiply:
  $$\frac{448\times 20}{207}$$
- step5: Multiply:
  $$\frac{8960}{207}$$
### Part (a): Percentage of criminals who pled guilty
The calculation gives us:

$$
\text{Percentage of guilty pleas} \approx 92.7\%
$$

### Part (b): Percentage of criminals sentenced to prison
First, we calculate the total number of criminals sentenced to prison:

$$
P = 396 + 52 = 448
$$

Now, we find the percentage of criminals sentenced to prison:

$$
\text{Percentage sentenced to prison} \approx \left( \frac{448}{1035} \right) \times 100 \approx 43.3\%
$$

### Final Answers:
- (a) The percentage of criminals who pled guilty is $$ 92.7\% $$.
- (b) The percentage of criminals sentenced to prison is $$ 43.3\% $$.
- (a) 92.7% of criminals pled guilty. - (b) 43.3% of criminals were sent to prison.

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