Final answer:
To find the fraction of students receiving a score of 70 or more, one can analyze percentiles, calculate probabilities for scenarios like guessing on a quiz, and use histograms to visualize score distributions and count the relevant intervals.
Step-by-step explanation:
To determine the fraction of students receiving a score of 70 or more, we can implement a few statistical methods. When dealing with percentiles, such as finding 'the 70th percentile', we are identifying a score below which a certain percentage of scores fall. If the 70th percentile score is 'k', then 70 percent of students scored lower than 'k' and 30 percent scored higher. In an example with test scores, if the 70th percentile is 16 on a 20-question test, it means that 70 percent of the students answered fewer than 16 questions correctly.
In scenarios where a student guesses on a true-false quiz, the probability of achieving a specific score can be calculated using the binomial probability formula. To pass with at least a 70 percent, a student would need to get at least 7 out of 10 questions correct. We use binomial probability because each question has two possible outcomes (true or false), and we assume each guess is independent of the others.
Finally, using histograms and other statistical data representation methods allow us to visualize the distribution of scores. For example, if a histogram shows the class boundaries and the number of students within those ranges, we can calculate the fraction of students scoring 70 or higher by adding up the counts in the relevant intervals.