Scores for a common standardized college aptitude test are normally distributed with a mean of 516 and a standard deviation of 96. Randomly selected men are given a Prepartion Course before taking this test. Assume, for sake of argument, that the Preparation Course has no effect on people's test scores. If 1 of the men is randomly selected, find the probability that his score is at least 546.8. P(X> 546.8) = Enter your answer as a number accurate to 4 decimal places. If 19 of the men are randomly selected, find the probability that their mean score is at least 546.8. P(x-bar> 546.8) = Enter your answer as a number accurate to 4 decimal places. If the random sample of 19 men does result in a mean score of 546.8, is there strong evidence to support a claim that the Preapartion Course is actually effective? (Use the criteria that "unusual" events have a probability of less than 5%.) O No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 546.8 if the Preparation Course has no effect. O Yes. The probability indicates that is is highly unlikely that by chance, a randomly selected group of students would get a mean as high as 546.8 if the Preparation Course has no effect.
Scores for a common standardized college aptitude test are normally distributed with a mean of 516 and a standard deviation of 96. Randomly selected men are given a Prepartion Course before taking this test. Assume, for sake of argument, that the Preparation Course has no effect on people's test scores. If 1 of the men is randomly selected, find the probability that his score is at least 546.8. P(X> 546.8) = Enter your answer as a number accurate to 4 decimal places. If 19 of the men are randomly selected, find the probability that their mean score is at least 546.8. P(x-bar> 546.8) = Enter your answer as a number accurate to 4 decimal places. If the random sample of 19 men does result in a mean score of 546.8, is there strong evidence to support a claim that the Preapartion Course is actually effective? (Use the criteria that "unusual" events have a probability of less than 5%.) O No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 546.8 if the Preparation Course has no effect. O Yes. The probability indicates that is is highly unlikely that by chance, a randomly selected group of students would get a mean as high as 546.8 if the Preparation Course has no effect.
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![### Probability and Statistics in Education
**Problem Description:**
Scores for a common standardized college aptitude test are normally distributed with a mean of 516 and a standard deviation of 96. Randomly selected men are given a Preparation Course before taking this test. Assume, for sake of argument, that the Preparation Course has no effect on people's test scores.
#### Task A:
- **Objective**: Find the probability that one man's score is at least 546.8.
- **Mathematical Expression**: \( P(X > 546.8) \)
- **Requirement**: Enter your answer as a number accurate to four decimal places.
\[ \begin{aligned}
P(X > 546.8) = \_\_\_\_
\end{aligned} \]
#### Task B:
- **Objective**: Find the probability that the mean score of 19 randomly selected men is at least 546.8.
- **Mathematical Expression**: \( P(\bar{x} > 546.8) \)
- **Requirement**: Enter your answer as a number accurate to four decimal places.
\[ \begin{aligned}
P(\bar{x} > 546.8) = \_\_\_\_
\end{aligned} \]
#### Analysis:
If the random sample of 19 men does result in a mean score of 546.8, we need to determine whether there is strong evidence to support the claim that the Preparation Course is actually effective. Use the criteria that "unusual" events have a probability of less than 5%.
**Choices:**
- **Option 1**: No. The probability indicates that it is possible by chance alone to randomly select a group of students with a mean as high as 546.8 if the Preparation Course has no effect.
- **Option 2**: Yes. The probability indicates that it is highly unlikely that by chance, a randomly selected group of students would get a mean as high as 546.8 if the Preparation Course has no effect.
**Response**:
_Select one of the given choices based on the calculated probabilities and your statistical interpretation._
This content and tasks are designed to help you understand the application of probability and normal distributions in evaluating the effectiveness of educational interventions. Analyzing whether a preparation course impacts standardized test scores can provide valuable insights into its value and effectiveness.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae9dff02-6614-4387-a434-63ee01638e81%2F84a6a65a-6ea8-476f-ba75-1d067f243a33%2Fzkp28j1q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability and Statistics in Education
**Problem Description:**
Scores for a common standardized college aptitude test are normally distributed with a mean of 516 and a standard deviation of 96. Randomly selected men are given a Preparation Course before taking this test. Assume, for sake of argument, that the Preparation Course has no effect on people's test scores.
#### Task A:
- **Objective**: Find the probability that one man's score is at least 546.8.
- **Mathematical Expression**: \( P(X > 546.8) \)
- **Requirement**: Enter your answer as a number accurate to four decimal places.
\[ \begin{aligned}
P(X > 546.8) = \_\_\_\_
\end{aligned} \]
#### Task B:
- **Objective**: Find the probability that the mean score of 19 randomly selected men is at least 546.8.
- **Mathematical Expression**: \( P(\bar{x} > 546.8) \)
- **Requirement**: Enter your answer as a number accurate to four decimal places.
\[ \begin{aligned}
P(\bar{x} > 546.8) = \_\_\_\_
\end{aligned} \]
#### Analysis:
If the random sample of 19 men does result in a mean score of 546.8, we need to determine whether there is strong evidence to support the claim that the Preparation Course is actually effective. Use the criteria that "unusual" events have a probability of less than 5%.
**Choices:**
- **Option 1**: No. The probability indicates that it is possible by chance alone to randomly select a group of students with a mean as high as 546.8 if the Preparation Course has no effect.
- **Option 2**: Yes. The probability indicates that it is highly unlikely that by chance, a randomly selected group of students would get a mean as high as 546.8 if the Preparation Course has no effect.
**Response**:
_Select one of the given choices based on the calculated probabilities and your statistical interpretation._
This content and tasks are designed to help you understand the application of probability and normal distributions in evaluating the effectiveness of educational interventions. Analyzing whether a preparation course impacts standardized test scores can provide valuable insights into its value and effectiveness.
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