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2. The College Board reports that in 2017, the mean math score was 544 and the standard deviation was 128 A sample of 55 scores was selected. a. What is the probability that the sample mean score is less than 500? M= 2419² 416 - M = 7.56 (2) b. What is the probability that the sample mean score is between 480 and 520? 11/ 400-5 1.1= 0.92 7 c. Find the 75th percentile of the sample mean? 37 1/1 M = 2.03 X X X = m - 40 soliqui

2. The College Board reports that in 2017, the mean math score was 544 and the standard deviation was 128 A sample of 55 scores was selected. a. What is the probability that the sample mean score is less than 500? M= 2419² 416 - M = 7.56 (2) b. What is the probability that the sample mean score is between 480 and 520? 11/ 400-5 1.1= 0.92 7 c. Find the 75th percentile of the sample mean? 37 1/1 M = 2.03 X X X = m - 40 soliqui

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Title: Understanding Sample Mean and Probability Calculations** The following exercises demonstrate how to calculate probabilities related to sample means, based on a sample of SAT math scores in 2017. The mean math score was 544 and the standard deviation was 128. A sample of 55 scores was selected. ### Exercise 2 #### a. Probability of a Sample Mean Score Less than 500 To determine the probability that the sample mean score is less than 500, use the following: 1. Calculate the z-score: - Mean (M) = 544, Standard Deviation = 128, Sample Size (n) = 55 - Sample Mean = 500 - Standard Error (SE) = 128 / √55 ≈ 17.23 - Z = (500 - 544) / SE = -44 / 17.23 ≈ -2.55 2. Probability (P) calculation using z-table: - P(Z < -2.55) (look up the value in a z-table) The handwritten work shows steps for the calculations, with values rounded and z-score formula applied. #### b. Probability that the Sample Mean Score is Between 480 and 520 Steps: 1. Calculate z-scores for both bounds (480 and 520): - Z for 480: (480 - 544) / 17.23 ≈ -3.72 - Z for 520: (520 - 544) / 17.23 ≈ -1.40 2. Find probabilities: - P(Z < 520) and P(Z < 480) from z-tables - Subtract to find the probability between two z-scores The handwritten work outlines these steps and the calculations for z-scores and probabilities. #### c. Find the 75th Percentile of the Sample Mean 1. Obtain the z-score for the 75th percentile (approximately 0.675 from the z-table). 2. Use the mean and standard deviation to find the score: - X = M + Z * SE = 544 + 0.675 * 17.23 ≈ 555.63 The handwritten work involves confirming these calculations with the percentile value from the z-table and applying it to find the actual score. ### Summary This problem set involves understanding the application of z-scores in finding probabilities and percentiles related
Transcribed Image Text:**Title: Understanding Sample Mean and Probability Calculations** The following exercises demonstrate how to calculate probabilities related to sample means, based on a sample of SAT math scores in 2017. The mean math score was 544 and the standard deviation was 128. A sample of 55 scores was selected. ### Exercise 2 #### a. Probability of a Sample Mean Score Less than 500 To determine the probability that the sample mean score is less than 500, use the following: 1. Calculate the z-score: - Mean (M) = 544, Standard Deviation = 128, Sample Size (n) = 55 - Sample Mean = 500 - Standard Error (SE) = 128 / √55 ≈ 17.23 - Z = (500 - 544) / SE = -44 / 17.23 ≈ -2.55 2. Probability (P) calculation using z-table: - P(Z < -2.55) (look up the value in a z-table) The handwritten work shows steps for the calculations, with values rounded and z-score formula applied. #### b. Probability that the Sample Mean Score is Between 480 and 520 Steps: 1. Calculate z-scores for both bounds (480 and 520): - Z for 480: (480 - 544) / 17.23 ≈ -3.72 - Z for 520: (520 - 544) / 17.23 ≈ -1.40 2. Find probabilities: - P(Z < 520) and P(Z < 480) from z-tables - Subtract to find the probability between two z-scores The handwritten work outlines these steps and the calculations for z-scores and probabilities. #### c. Find the 75th Percentile of the Sample Mean 1. Obtain the z-score for the 75th percentile (approximately 0.675 from the z-table). 2. Use the mean and standard deviation to find the score: - X = M + Z * SE = 544 + 0.675 * 17.23 ≈ 555.63 The handwritten work involves confirming these calculations with the percentile value from the z-table and applying it to find the actual score. ### Summary This problem set involves understanding the application of z-scores in finding probabilities and percentiles related
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