14. A recent survey of universities and colleges in each state was conducted. The number of univer- sities and colleges was recorded for each of the fifty states. A histogram of the results is given in Figure 7.2 (a) States with the highest amount of colleges and universities fall within what range? Figure 7.2: Number of colleges and universities in each of the fifty states (b) It is most common for a state to have what number of universities? That is, give the range represented by the mode. (c) Approximately how many states have at least 400 uiversities? 25 (d) Approximately what proportion of states have at least 400 universities? 10 (e) Approximately what proportion of states have at most 200 universities? 1000 1200 1400 600 800 400 200 Number of Colleges and Universities 15. The site data.cms.gov provides data on average expenditures for medical procedures across the nation. The histogram in Figure 7.3 displays Medicare payments for patients with septicemia or severe sepsis in a random sample of thirty-six hospitals. Figure 7.3: Medicare payments for sepsis patients at 36 hospitals (a) Describe the key features of the histogram. (b) Approximately what percent of Medicare payments for sepsis are at most $10,000? (c) Approximately what percent of Medicare payments for sepsis are at least $13,000? 14000 18000 16000 12000 10000 8000 Medicare Payments (dollars) Frequency Frequency 2 5 15 20 35 4. 9.

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.