A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Transcribed Image Text:Suppose that the amount of time that students spend
studying in the library in one sitting is normally distributed
with mean 42 minutes and standard deviation 21 minutes. A
researcher observed 45 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( 42
21
b. What is the distribution of x? x N 42
~
3.1305
c. What is the distribution of Σæ? Σx - N
x? Xx
d. If one randomly selected student is timed, find the
probability that this student's time will be between 38
and 42 minutes.
e. For the 45 students, find the probability that their
average time studying is between 38 and 42 minutes.
f. Find the probability that the randomly selected 45
students will have a total study time more than 1665
minutes.
g. For part e) and f), is the assumption of normal
necessary? No Yes
h. The top 15% of the total study time for groups of 45
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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