113 7.7 Topic 7: The Normal Distribution 00. Suppose a population is unimodal and symmetric with mean 55 and standard deviation 7. Use Figure 7.11 to aid in answering the following questions. (a) Approximately what percent of observations are below 34? (b) Approximately what percent of observations are above 55? (c) Approximately what percent of observations are between 41 and 62? (d) Approximately what percent of observations are above 48? Figure 7.11: Depiction of the Empirical Rule for X N(55, 7) X: 34 41 48 55 62 69 76 Z: -3 -2 -1 2 57. Consider the standard normal distribution, Z ~ N(0, 1). Find the following using the calculator. (a) The area below z = 1.3. (b) The area below z =-1.3. (c) The area above z = 1.3. %3D (d) The area between z = -1.3 and z = 1.3. 58. Suppose times for the 100m sprint for the average person are unimodal and symmetric with mean 14 seconds and standard deviation 0.8 seconds. What is the probability that the average person has a time faster than Usain Bolt's record of 9.58 seconds? 59. Consider the standard normal distribution, Z ~ N(0, 1). Find the following using the calculator. (a) The z-score of the 45th percentile. 60. Suppose times for the 100m sprint for the average person are unimodal and symmetric with mean 14 seconds and standard deviation 0.8 seconds. What speed is the third quartile? Hint: The third quartile represents what percentile? (b) The z-score for the top 20%. 3.

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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.