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 22 minutes. A researcher observed 18 students who entered the library to study. Round all answers to 4 decimal places where possible.What is the distribution of XX? XX ~ N(,)What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)What is the distribution of ∑x∑x? ∑x∑x ~ N(,)If one randomly selected student is timed, find the probability that this student's time will be between 40 and 47 minutes. For the 18 students, find the probability that their average time studying is between 40 and 47 minutes. Find the probability that the randomly selected 18 students will have a total study time more than 684 minutes. For part e) and f), is the assumption of normal necessary? -No -YesThe top 10% of the total study time for groups of 18 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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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 42 minutes and standard deviation 22 minutes. A researcher observed 18 students who entered the library to study. Round all answers to 4 decimal places where possible.

What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
If one randomly selected student is timed, find the probability that this student's time will be between 40 and 47 minutes.
For the 18 students, find the probability that their average time studying is between 40 and 47 minutes.
Find the probability that the randomly selected 18 students will have a total study time more than 684 minutes.
For part e) and f), is the assumption of normal necessary? -No -Yes
The top 10% of the total study time for groups of 18 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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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