Empirical Rule. For data having a bell-shaped (normal) distribution: ± contains

Question

Empirical Rule. For data having a bell-shaped (normal) distribution: ± contains approximately 68% of the measurements. 2 contains approximately 95% of the measurements. 3o contains almost all of the measurements. 2-score. The z-score fori(,-). 3. Consider a sample with data 10, 20, 12, 17, and 16. Compute the mean and standard deviation. Compute the z-score for r 20 4. Consider a sample with mean of 500 and standard deviation of 100. What is the z-score for-520 5. Suppose the data have a bell-shaped distribution with a mean of 30 and standard deviation of 5. Use the empirical rule to determine the percentage of data within each of the following ranges: a. 20 to 40 b. 15 to 45 c. 25 to 35 Chapter 4.I Set. A set is a element of the set. For two sets A and B, we say A is a subset of B, denoted Ac B, if every element in A is also in B. The empty set, denoted by 0, is the set consisting of no elements. The union of A and B, denoted by AUB, is the set of all elements in A or B. The intersection of A and B, denoted by AnB, is the set of all elements in both A and B. Two set A and B are said to be disjoint if AnB-0. For ACS (universal set), the complement of A, denoted by A", is the ion to Probability n of objects. A member of the collection is also called an set of all elements in S but not in A. Random Experiment. An experiment is the process by which an observation is made. The sample space for an experiment is the set of all possible outcomes; each outcome is called a sample point. An event is a collection of sample points, that is, any subset of the sample space. An event that contains only one sample point is called a simple event. Two events are called mutually exclusive if their intersection is empty. Assign Probability. Let S be a sample space. For every event A in S, we assign a number P(A), called the probability of A, so that 1. P(A)20. 2. P(S)-1 3. P(A,UAzU.) PIA.), where A, A2,... are pairwise mutually exclhusive. Review the classical method, relative frequency method, and subjective method for Product Rule (Multiple-step experiments). If an experiment can be described as a sequence of 2 steps with ni outcomes on the first step and na outcomes on the second step, then the total number of outcomes is rn n2 Permutation. The number of ways of ordering n objects taken r at a time is nl

Explanation / Answer

#3.
mean = 15
std. dev. = 4

z = (20 - 15)/4 = 1.25

#4.
z = (500 - 520)/100 = 0.2

#5.
mean = 30, sd = 5

a)
(30 - 2*5, 30 + 2*5) = (20 , 40)
Hence 95% of data lies within 20 to 40

b)
(30 - 3*5, 30 + 3*5) = (15 , 45)
Hence almost all of data lies within 15 to 45

c)
(30 - 5, 30 + 5) = (25 , 35)
Hence 68% of data lies within 25 to 35

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