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on or 2.5. a. Fill out the following curves for each distribution. Be sure to label your set of numbers which is for which exam. You can give your answers as a list of values. Explain your values. b. What is the probability that a randomly selected student scored less than a 14.5 on the ACT English Test? Explain. c. What is the probability that a randomly selected student scored more than a 650 on the SAT Verbal Test? Explain.

on or 2.5. a. Fill out the following curves for each distribution. Be sure to label your set of numbers which is for which exam. You can give your answers as a list of values. Explain your values. b. What is the probability that a randomly selected student scored less than a 14.5 on the ACT English Test? Explain. c. What is the probability that a randomly selected student scored more than a 650 on the SAT Verbal Test? Explain.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Understanding Distribution and Probability in Standardized Test Scores** The SAT Verbal Test in recent years followed approximately a normal distribution with a mean of 460 and a standard deviation of 110. The scores on the ACT English Test follow approximately a normal distribution with a mean of 17 and a standard deviation of 2.5. **a. Fill out the following curves for each distribution. Be sure to label your set of numbers which is for which exam. You can give your answers as a list of values. Explain your values.** To label the curves correctly using the properties of normal distribution, we consider the mean and standard deviations: *For the SAT Verbal Test:* - Mean = 460 - Standard Deviation = 110 The values at each tick mark on the horizontal axis typically represent: - Mean - 3σ: \(460 - 3 \times 110 = 130\) - Mean - 2σ: \(460 - 2 \times 110 = 240\) - Mean - 1σ: \(460 - 1 \times 110 = 350\) - Mean: \(460\) - Mean + 1σ: \(460 + 1 \times 110 = 570\) - Mean + 2σ: \(460 + 2 \times 110 = 680\) - Mean + 3σ: \(460 + 3 \times 110 = 790\) *For the ACT English Test:* - Mean = 17 - Standard Deviation = 2.5 The values at each tick mark on the horizontal axis typically represent: - Mean - 3σ: \(17 - 3 \times 2.5 = 9.5\) - Mean - 2σ: \(17 - 2 \times 2.5 = 12\) - Mean - 1σ: \(17 - 1 \times 2.5 = 14.5\) - Mean: \(17\) - Mean + 1σ: \(17 + 1 \times 2.5 = 19.5\) - Mean + 2σ: \(17 + 2 \times 2.5 = 22\) - Mean + 3σ: \(17 + 3 \times 2.5 = 24.5\) **b. What is the probability that a randomly selected student
Transcribed Image Text:**Understanding Distribution and Probability in Standardized Test Scores** The SAT Verbal Test in recent years followed approximately a normal distribution with a mean of 460 and a standard deviation of 110. The scores on the ACT English Test follow approximately a normal distribution with a mean of 17 and a standard deviation of 2.5. **a. Fill out the following curves for each distribution. Be sure to label your set of numbers which is for which exam. You can give your answers as a list of values. Explain your values.** To label the curves correctly using the properties of normal distribution, we consider the mean and standard deviations: *For the SAT Verbal Test:* - Mean = 460 - Standard Deviation = 110 The values at each tick mark on the horizontal axis typically represent: - Mean - 3σ: \(460 - 3 \times 110 = 130\) - Mean - 2σ: \(460 - 2 \times 110 = 240\) - Mean - 1σ: \(460 - 1 \times 110 = 350\) - Mean: \(460\) - Mean + 1σ: \(460 + 1 \times 110 = 570\) - Mean + 2σ: \(460 + 2 \times 110 = 680\) - Mean + 3σ: \(460 + 3 \times 110 = 790\) *For the ACT English Test:* - Mean = 17 - Standard Deviation = 2.5 The values at each tick mark on the horizontal axis typically represent: - Mean - 3σ: \(17 - 3 \times 2.5 = 9.5\) - Mean - 2σ: \(17 - 2 \times 2.5 = 12\) - Mean - 1σ: \(17 - 1 \times 2.5 = 14.5\) - Mean: \(17\) - Mean + 1σ: \(17 + 1 \times 2.5 = 19.5\) - Mean + 2σ: \(17 + 2 \times 2.5 = 22\) - Mean + 3σ: \(17 + 3 \times 2.5 = 24.5\) **b. What is the probability that a randomly selected student
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