Prob-Stats-Teacher-Book.pdf

# The probability that someone scores over 600 about

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The probability that someone scores over 600 About 0.16. Since 68% is in the middle, this leaves 32% in the 2 tails. We want the upper tail which is exactly half of 32% since the normal model is symmetrical 3. The probability that someone scores over 650 Z-score = 1.5 Answer: 0.0668 2 methods using calculator are shown to the right 4. The probability that someone scores between 450 and 600 Between z-scores of -0.5 and 1 Answer: 0.532 5. The probability that someone scores less than 420 Z-score of -0.8 Answer: 0.222 Practice Exercise 2 (p. 21) Suppose the data looking at insurance claims of oceanfront homes due to a category 3 hurricane are appropriately modeled by a normal curve with a mean of 99 (thousand) and a standard deviation of 21 (thousand). 1. If a category 3 hurricane hits, what is the probability that a particular household files a claim for more than \$110,000? Z-score = 11/21 = 0.5238 Answer: about 0.3

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MODULE 2 Page 13 2. What is the probability that a particular household files a claim for more than \$150,000? Z-score = 2.43 Answer = 0.00758 3. What is the probability that a particular household files a claim for less than \$90,000? Z-score = -0.429 Answer = 0.334 4. What claim would represent the 90th percentile? Z-score = -1.28 Answer: about \$125, 913 5. Approximately 5% of all claims would be below what amount? Z-score = -1.645 Answer: about \$64,458
Page 14 MODULE 3 Module 3: Discrete Probability Distributions In this module, students will learn about discrete probability distributions. They will compute value and standard deviation of a probability distribution and use this information to understand how much an insurance company might need to pay out if a hurricane hits Happy Shores. Content Learning Objectives Through the use of historical data about hurricanes and Happy Shores, students will be able to do the following: ± Estimate probabilities based on historical empirical data. ± Construct a probability distribution (probability model) for a discrete situation. ± Compute and interpret the expected value of a discrete probability distribution. ± Compute and interpret the standard deviation of a discrete probability distribution. Contextual Learning Objectives Using the content, students will be able to do the following: ± Estimate probabilities of different level storms hitting Happy Shores based on historical data. ± Find the expected damage a hurricane may cause along with the standard deviation. This will be done for each category of storm and neighborhood within Happy Shores. Common Core State Standards for Mathematics Using Probability to Make Decisions (S-MD) ± Calculate expected values and use them to solve problems. 1. Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using graphical displays as for data distributions.

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