Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 45 minutes and standard deviation 20 minutes. A researcher observed 17 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( 45 b. What is the distribution of ? - N 45 | 4.8507 c. What is the distribution of z? I- N( 765 82.4621 d. If one randomly selected student is timed, find the probability that this student's time will be between 47 and 50 minutes. e. For the 17 students, find the probability that their average time studying is between 47 and 50 minutes. f. Find the probability that the randomly selected 17 students will have a total study time less than 884 minutes. g. For part e) and f), is the assumption of normal necessary? O NoO Yes h. The top 10% of the total study time for groups of 17 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 Hint:
Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 45 minutes and standard deviation 20 minutes. A researcher observed 17 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( 45 b. What is the distribution of ? - N 45 | 4.8507 c. What is the distribution of z? I- N( 765 82.4621 d. If one randomly selected student is timed, find the probability that this student's time will be between 47 and 50 minutes. e. For the 17 students, find the probability that their average time studying is between 47 and 50 minutes. f. Find the probability that the randomly selected 17 students will have a total study time less than 884 minutes. g. For part e) and f), is the assumption of normal necessary? O NoO Yes h. The top 10% of the total study time for groups of 17 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 Hint:
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 45 minutes and standard deviation 20 minutes. Aresearcher observed 17 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 45
b. What is the distribution of ? I - N 45
4.8507
c. What is the distribution of r? I- N( 765
82.4621
d. If one randomly selected student is timed, find the probability that this student's time will be
between 47 and 50 minutes.
e. For the 17 students, find the probability that their average time studying is between 47 and 50
minutes.
f. Find the probability that the randomly selected 17 students will have a total study time less than 884
minutes.
g. For part e) and f), is the assumption of normal necessary? O NoO Yes
h. The top 10% of the total study time for groups of 17 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
Hìnt:
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