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Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 40 minutes and standard deviation 16 minutes. A researcher observed 47 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of a? - N( c. What is the distribution of > x? ) x - N(

Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 40 minutes and standard deviation 16 minutes. A researcher observed 47 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of a? - N( c. What is the distribution of > x? ) x - N(

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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Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 40 minutes and standard deviation 16 minutes. A researcher observed 47 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of æ? ¤ - N( c. What is the distribution of ) x? >x - N( d. If one randomly selected student is timed, find the probability that this student's time will be between 41 and 42 minutes. e. For the 47 students, find the probability that their average time studying is between 41 and 42 minutes. f. Find the probability that the randomly selected 47 students will have a total study time more than 1974 minutes. g. For part e) and f), is the assumption of normal necessary? O Yes No h. The top 10% of the total study time for groups of 47 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker? minutes
Transcribed Image Text:Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 40 minutes and standard deviation 16 minutes. A researcher observed 47 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of æ? ¤ - N( c. What is the distribution of ) x? >x - N( d. If one randomly selected student is timed, find the probability that this student's time will be between 41 and 42 minutes. e. For the 47 students, find the probability that their average time studying is between 41 and 42 minutes. f. Find the probability that the randomly selected 47 students will have a total study time more than 1974 minutes. g. For part e) and f), is the assumption of normal necessary? O Yes No h. The top 10% of the total study time for groups of 47 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker? minutes
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