105 20. People with diabetes must monitor and control their blood glucose level. The goal is to maintain "fasting plasma glucose" between 90 and 130 milligrams per deciliter (mg/dl). The fasting plasma glucose levels for 18 diabetics enrolled in a diabetes control class (five months after the class ends) are presented below. (a) What is the five number summary for this data? 141 158 112 153 134 95 (b) Check if there are outliers in the data. 96 78 148 172 200 271 103 172 (c) Draw a modified boxplot. 359 145 147 255 27. Suppose X is unimodal and symmetric with mean 10 and standard deviation 1. Answer the following questions with the help of Figure 7.7. (a) Approximately, what percent of observa- tions are between 9 and 11? Figure 7.7: The Empirical Rule (b) Approximately, what percent of observa- tions are between 9 and 12? (c) Approximately what percent of observa- tions are less than 9? (d) Approximately what percent of observa- tions are greater than 13? (e) What is the 84th percentile for X? (f) What is the 16th percentile for X? X: 7 10 11 12 13 Z: -3 -2 -1 3. 28. Suppose that the amount of sleep college students get per night has a symmetric, bell shaped distribution with mean 6.9 hours and standard deviation of 1.7 hours. (a) Between what two amounts of sleep do the middle 68% of students get? (b) What value is the 97.5th percentile? (c) What percent of values fall between 6.9 hours and 10.3 hours? (d) Would three hours of sleep be an unusual amount? Explain. 29. Calves born of the common dolphin (delphis) are 32 inches long on average with a standard deviation of about 0.75 inches. Suppose the lengths of the calves are bell shaped. (a) What length places a calf in the 2.5th percentile? The 50th percentile? (b) What percent of calves are at least 33.5 inches long? (c) What percent of calves are between 30.5 and 33.5 inches long? (d) Would it be unusual to have a calf born 35 inches long? Explain. 2.

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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.