Pacing Guide
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March 6 Homework Solutions Math 151, Winter 2012 Chapter 6 Problems (pages 287-291) Problem 31 According to the U.S. National Center for Health Statistics, 25.2 percent of males and 23.6 percent of females never eat breakfast. Suppose that random samples of 200 men and 200 women are chosen. Approximate the probability that (a) at least 110 of these 400 people never eat breakfast. Let M denote the number of men that never eat breakfast and W denote the number of women that never eat breakfast. Note that M is a binomial random variable with p = .252 and n = 200, and W is a binomial random variable with p = .236 and n = 200. We compute E[M ] = 200(.252) = 50.4, Var(M ) = 200(.252)(1 - .252) ≈ 37.7, E[W ] = 200(.236) = 47.2, Var(M ) = 200(.236)(1 - .236) ≈ 36.1. Thus we may approximate M by a normal random variable with μ = 50.4 and σ 2 ≈ 37.7 and we may approximate W by a normal random variable with μ = 47.2 and σ 2 ≈ 36.1. We want to compute P {110 ≤ M + W }. We may approximate M + W by a normal distribution with μ = 50.4 + 47.2 = 97.6 and σ 2 ≈ 37.7 + 36.1 = 73.8. Hence P {110 ≤ M + W } = P 110 - 97.6 √ 73.8 ≤ M + W - 97.6 √ 73.8 ≈ 1 - Φ 110 - 97.6 √ 73.8 ≈ 1 - Φ(1.44) = 1 - .9251 = .0749. (b) the number of the women who never eat breakfast is at least as large as the number of the men who never eat breakfast. We want to compute P {M ≤ W } = P {M - W ≤ 0}. We may approximate M - W by a normal distribution with μ = 50.4 - 47.2=3.2 and σ 2 = 37.7 + 36.1 = 73.8. Hence P {M ≤ W } = P {M - W ≤ 0} = P M - W - 3.2 √ 73.8 ≥ -3.2 √ 73.8 ≈ Φ -3.2 √ 73.8 ≈ 1 - Φ(.37) = 1 - .6443 = .3557. Problem 44 If X 1 , X 2 , X 3 are independent random variables that are uniformly distributed over (0, 1), compute the probability that the largest of the three is greater than the sum of the other two. 1
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Pacing Guide
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CCNA EXPLORATION V4.0
ROUTING PROTOCOLS AND CONCEPTS
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Prepared by Cisco Learning Institute
May 1, 2008
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May 1, 2008 Page 1
CCNA EXPLORATION: ROUTING PROTOCOLS AND CONCEPTS The Pacing Guide is a resource designed to maximize student learning. The Guide provides guidance on time management and difficulty level for Academy instructors teaching CCNA Exploration: Routing Protocols and Concepts. This Guide provides a suggested percentage of time to be spent on each chapter, based on both a two-month and four-month teaching cycle. It also recommends what percentage of time, within each chapter, should be spent on Lab activities. This assumes that instructors would use the remaining percentage of time outside of Lab activities on teaching, reading, discussion and/or assessment. For example, Chapter 1, Introduction to Routing and Packet Forwarding, is suggested to be completed within the first month, with 15% of instruction on Lab activities. Also provided in the Guide is the difficulty level of each chapter based on data from student exam scores and instructor feedback. This provides insight into the difficulty level of teaching the material, as well as identifies material that students may have a difficult time grasping. The difficulty level is ranked as High (H), Moderate (M), or Low (L).
CCNA Exploration: Routing Protocols and Concepts
Teaching Cycle Difficulty Level
Chapters % of Time to Be Spent on Each
Chapter
Minimum % of Time to Be Spent
on Labs 2 Months 4 Months H M L
1. Introduction to Routing and Packet Forwarding
10% 20%
2. Static Routing 10% 20%
1st month
3. Introduction to Dynamic Routing Protocols
10% 15%
4. Distance Vector Routing Protocols 5% 5%
5. RIP version 1 10% 20%
1st month
2nd month
6. VLSM and CIDR 10% 25%
7. RIPv2 10% 20%
8. The Routing Table: A Closer Look 10% 15%
3rd month
9. EIGRP 10% 15%
10. Link-State Routing Protocols 5% 0%
11. OSPF 10% 15%
2nd month
4th month
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