i. 6 fomework Part 4 of 4 Poincs 0 or 1 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 guilfy, 52 were sent to prison. Complete (a) through (d). a. What percentage of the criminals pled guity? $$ 927 \% $$ (Round to the nearest tenth as needed) b. What percentage of the criminals were sent to prison? $$ 433 \% $$ (Round to the nearest tentif as needed) c. Among those who pled guilty, what is the percentage who were sent to prison? $$ 41.3 \% $$ (Round to the nearest tenth as needed) d. Among those who pled not guity, what is the percentage who were sentlo prison? $$ \square $$ \% (Round to the nearest tenth as needed)

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Let's solve each part step by step.

### Given Data:
- Total criminals: $$ N = 1035 $$
- Criminals who pled guilty: $$ G = 959 $$
- Criminals sentenced to prison who pled guilty: $$ P_G = 396 $$
- Criminals who pled not guilty: $$ N_G = 76 $$ (calculated as $$ N - G $$)
- Criminals sentenced to prison who pled not guilty: $$ P_N = 52 $$

### a. What percentage of the criminals 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 values:

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

### b. What percentage of the criminals were sent to prison?
To find the percentage of criminals who were sent to prison, we first calculate the total number of criminals sent to prison:

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

Then, we use the formula:

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

### c. Among those who pled guilty, what is the percentage who were sent to prison?
To find the percentage of guilty pleas that resulted in prison sentences, we use the formula:

$$
\text{Percentage of guilty pleas sent to prison} = \left( \frac{P_G}{G} \right) \times 100
$$

### d. Among those who pled not guilty, what is the percentage who were sent to prison?
To find the percentage of not guilty pleas that resulted in prison sentences, we use the formula:

$$
\text{Percentage of not guilty pleas sent to prison} = \left( \frac{P_N}{N_G} \right) \times 100
$$

Now, let's perform the calculations for parts a, b, c, and d.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{396}{959}\times 100$$
- step1: Multiply:
  $$\frac{396\times 100}{959}$$
- step2: Multiply:
  $$\frac{39600}{959}$$
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:
  $$\frac{8960}{207}$$
Calculate or simplify the expression $$ (52/76)*100 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{52}{76}\right)\times 100$$
- step1: Reduce the fraction:
  $$\frac{13}{19}\times 100$$
- step2: Multiply:
  $$\frac{13\times 100}{19}$$
- step3: Multiply:
  $$\frac{1300}{19}$$
Calculate or simplify the expression $$ (959/1035)*100 $$.
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:
  $$\frac{19180}{207}$$
Now, let's summarize the results for each part:

### a. What percentage of the criminals pled guilty?
$$
\text{Percentage of guilty pleas} \approx 92.7\%
$$

### b. What percentage of the criminals were sent to prison?
$$
\text{Percentage sent to prison} \approx 43.3\%
$$

### c. Among those who pled guilty, what is the percentage who were sent to prison?
$$
\text{Percentage of guilty pleas sent to prison} \approx 41.3\%
$$

### d. Among those who pled not guilty, what is the percentage who were sent to prison?
$$
\text{Percentage of not guilty pleas sent to prison} \approx 68.4\%
$$

### Final Answers:
- a. $$ 92.7\% $$
- b. $$ 43.3\% $$
- c. $$ 41.3\% $$
- d. $$ 68.4\% $$
- a. 92.7% - b. 43.3% - c. 41.3% - d. 68.4%

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