Please help with the question
The data in the following table show the outcomes of guilty and not-guilty pleas in 1,031 criminal court cases. What is the probability that a randomly selected defendant either pled guilty or was sent to prison?
The probability that a randomly selected defendant either pled guilty or was sent to prison is __. (Round to the nearest thousandth as needed.)
No table shown.
Guilty plea Not-guilty plea
Sent to prison 383 63
Not sent to prison 569 16
To find the probability that a randomly selected defendant either pled guilty or was sent to prison, we need to determine the number of cases where the defendant either pled guilty or was sent to prison and divide it by the total number of cases.
Looking at the information provided in the table, it's important to note that the table only provides outcomes for guilty and not-guilty pleas. We don't have specific data on the number of defendants sent to prison. Therefore, we need to make an assumption that all defendants who did not plead guilty were sent to prison.
Let's calculate the probability step by step:
1. Determine the number of cases where the defendant pled guilty:
- From the table, find the "Guilty" column and sum up the values:
Guilty: 590
2. Determine the number of cases where the defendant was sent to prison:
- Since we assume that all defendants who did not plead guilty were sent to prison, we need to subtract the number of guilty pleas from the total number of cases:
Total cases: 1,031
Cases where the defendant pled guilty: 590
Not guilty cases = Total cases - Guilty cases
= 1,031 - 590
= 441
Therefore, the number of cases where the defendant was sent to prison is 441.
3. Calculate the probability:
- To get the probability, we divide the sum of guilty pleas and cases where the defendant was sent to prison by the total number of cases:
Probability = (Guilty cases + Cases sent to prison) / Total cases
= (590 + 441) / 1,031
Now, solving the expression, we get:
Probability ≈ 1.019
Round to the nearest thousandth, the probability that a randomly selected defendant either pled guilty or was sent to prison is approximately 1.019.
Determine whether the statement below makes sense or does not make sense. Explain clearly.
Based on our sample, the 95% confidence interval for the mean amount of television watched by adults in a nation is 2.9 to 3.5 hours per day. Therefore, there is 95% chance that the mean for all adults in the nation will fall somewhere in this range and a 5% chance that it will not.