Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 46 minutes and standard deviation 23 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( b. What is the distribution of ? a - N( c. What is the distribution of > x? x - N

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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 46 minutes and standard deviation 23 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(
b. What is the distribution of a? a - 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 47 and 54 minutes.
e. For the 17 students, find the probability that their average time studying is between 47 and 54
minutes.
f. Find the probability that the randomly selected 17 students will have a total study time more than
816 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
Transcribed Image Text:Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 46 minutes and standard deviation 23 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( b. What is the distribution of a? a - 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 47 and 54 minutes. e. For the 17 students, find the probability that their average time studying is between 47 and 54 minutes. f. Find the probability that the randomly selected 17 students will have a total study time more than 816 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
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