Select a first-year college student at random and ask what his or her academic rank was in high probabilities, based on proportions from a large sample survey of first year students: Rank Top Probability Top 20% 0.41 Second 20% 0.23 Third 20% 0.29 Fourth 20% 0.06 cmillan L & Pthe first was in the top 20% and the second was in the lowest 20%) =
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High school academic rank. Selected first-year college student at random and ask what his or her academic rank was in high school: Here are the probabilities, based on proportions from a large sample survey of first-year college students: (Show your work for credit) Rank probability Top 20% 0.41 Second 20% 0.23 Third 20% 0.29 Fourth 20% 0.06 Lowest 20% 0.01 Is this a legitimate probability model? What is the probability that a randomly chosen first-year college student was in the top 20% of his or her high school class? What is the probability that a randomly chosen first-year college student was in the top 40% of his or her high school class? What is the probability that a randomly chosen first-year college student was not in the top 20% of his or her high school class?
Donna D.
The grades of a freshman college class, obtained after the first year of college, were analyzed. Seventy percent of the students in the top quarter of the college class had graduated in the upper 10% of their high school class, as had 50% of the students in the middle half of the college class and 20% of the students in the bottom quarter of the college class. a. What is the probability that a randomly chosen freshman graduated in the upper 10% of his high school class? b. What is the probability that a randomly chosen freshman who graduated in the upper 10% of the high school class will be in the top quarter of the college class? c. What is the probability that a randomly chosen freshman who did not graduate in the upper 10% of the high school class will not be in the top quarter of the college class?
Lucas F.
The table gives the results of a survey of $282,549$ freshmen from a recent class year at 437 of the nation's baccalaureate colleges and universities. $$\begin{array}{|lc|c|c|c|} \hline \begin{array}{l} \text { Number of Colleges } \\ \text { Applied to } \end{array} & 1 & 2 \text { or } 3 & 4-6 & 7 \text { or more } \\ \hline \begin{array}{l} \text { Percent (as a } \\ \text { decimal) }The student applied to fewer than 4 colleges. \end{array} & 0.20 & 0.29 & 0.37 & 0.14 \end{array}$$$$\begin{aligned} &\text {Using the percents as probabilities, find the probability of}\\ &\text { each event for a randomly selected student.} \end{aligned}$$
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