Final answer:
The inquiries revolve around predicting exam scores, calculating the probability of passing a true-false quiz by guessing, understanding 95 percent confidence intervals, determining sample sizes for surveys to estimate proportions, and conducting hypothesis tests for rates of behavior.
Step-by-step explanation:
The student's questions primarily pertain to probability and statistics, which are important concepts within the field of mathematics, particularly in data analysis and interpretation. When seeking to predict outcomes or verify claims, statisticians use various methods to estimate probabilities and calculate confidence intervals.
Predicting Exam Scores
If we have previous data or a model that correlates third exam scores with final exam scores, we could use it to predict the final exam score for a student who scored a 90 on the third exam. However, without such a model or additional information, a prediction cannot be made accurately.
Probability of Passing a Quiz
The probability of passing a 10-question true-false quiz by guessing randomly on each answer, would involve calculating the likelihood of getting at least 7 questions correct (a 70 percent score) which follows a binomial distribution.
95 Percent Confidence Interval
A 95 percent confidence interval does not imply that it contains 95 percent of the data, but rather that there is a 95 percent probability that the interval will capture the true population parameter. In practice, we would use statistical methods to calculate the interval based on a sample and then see if the expected percentage of data falls within that range.
Political Awareness Survey
When estimating the true proportion of students who voted with a specified level of confidence and margin of error, we can use sample size calculation formulas specific to proportion estimates. This incorporates the desired margin of error, the confidence level, and an estimated proportion, if available.
Hypothesis Testing
A hypothesis test would be conducted to determine whether there is a significant difference between a known rate and one observed in a survey. This involves comparing observed data with the expected rate under a null hypothesis.