Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 48 minutes and standard deviation 21 minutes. A researcher observed 14 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( 48 21 b. What is the distribution of ? - N( 48 5.6125 c. What is the distribution of ) x? )`. x - N( 672 78.574 ) a d. If one randomly selected student is timed, find the probability that this student's time will be between 45 and 48 minutes. 0.016 e. For the 14 students, find the probability that their average time studying is between 45 and 48 minutes. f. Find the probability that the randomly selected 14 students will have a total study time less than 728 minutes. g. For part e) and f), is the assumption of normal necessary? O YesO No h. The top 20% of the total study time for groups of 14 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: Some Helpful Videos:
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Given information
Mean µ = 48
Standard deviation σ = 21
Sample size n = 14
d)
If one randomly selected student is timed, Probability that this students time will be between 45 and 48 minutes is given by
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