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2. Scores on a mathematics exam given to ten-year-old children throughout Japan are Normally distributed with a mean of 520 and a standard deviation of 50. Suppose that each classroom with 25 students can be considered a random sample of 25 students from the population taking the exam. One of these classes can be selected at random and X would be the average score of the 25 students in that classroom (the sample mean). a) a) What is the mean or expected value of X, H, equal to? b) The standard deviation of X,0,, is a measure of how much you'd expect X to vary from classroom to classroom (assuming each classroom had 25 students randomly selected from the entire population), find Oz. b) c) What proportion of classrooms with 25 students would be expected to have a mean score, X, that is between 520 and 555? c) d) What proportion of classrooms with 25 students would be expected to have a mean score, X, that is below 500? d) e) Only the top 4% of classrooms with 25 students will have an average score which is above

2. Scores on a mathematics exam given to ten-year-old children throughout Japan are Normally distributed with a mean of 520 and a standard deviation of 50. Suppose that each classroom with 25 students can be considered a random sample of 25 students from the population taking the exam. One of these classes can be selected at random and X would be the average score of the 25 students in that classroom (the sample mean). a) a) What is the mean or expected value of X, H, equal to? b) The standard deviation of X,0,, is a measure of how much you'd expect X to vary from classroom to classroom (assuming each classroom had 25 students randomly selected from the entire population), find Oz. b) c) What proportion of classrooms with 25 students would be expected to have a mean score, X, that is between 520 and 555? c) d) What proportion of classrooms with 25 students would be expected to have a mean score, X, that is below 500? d) e) Only the top 4% of classrooms with 25 students will have an average score which is above

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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2. Scores on a mathematics exam given to ten-year-old children throughout Japan are Normally distributed with a mean of 520 and a standard deviation of 50. Suppose that each classroom with 25 students can be considered a random sample of 25 students from the population taking the exam. One of these classes can be selected at random and X would be the average score of the 25 students in that classroom (the sample mean). a) a) What is the mean or expected value of X, H, equal to? b) The standard deviation of X,0,, is a measure of how much you'd expect X to vary from classroom to classroom (assuming each classroom had 25 students randomly selected from the entire population), find Oz. b)
Transcribed Image Text:2. Scores on a mathematics exam given to ten-year-old children throughout Japan are Normally distributed with a mean of 520 and a standard deviation of 50. Suppose that each classroom with 25 students can be considered a random sample of 25 students from the population taking the exam. One of these classes can be selected at random and X would be the average score of the 25 students in that classroom (the sample mean). a) a) What is the mean or expected value of X, H, equal to? b) The standard deviation of X,0,, is a measure of how much you'd expect X to vary from classroom to classroom (assuming each classroom had 25 students randomly selected from the entire population), find Oz. b)
c) What proportion of classrooms with 25 students would be expected to have a mean score, X, that is between 520 and 555? c) d) What proportion of classrooms with 25 students would be expected to have a mean score, X, that is below 500? d) e) Only the top 4% of classrooms with 25 students will have an average score which is above
Transcribed Image Text:c) What proportion of classrooms with 25 students would be expected to have a mean score, X, that is between 520 and 555? c) d) What proportion of classrooms with 25 students would be expected to have a mean score, X, that is below 500? d) e) Only the top 4% of classrooms with 25 students will have an average score which is above
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