Answered: Suppose that the amount of time that…

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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Question

chapter test , question 8, part 1

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 7 students who entered the library to study. Round all answers to 6 decimal places where possible.

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 41 and 49 minutes.
For the 7 students, find the probability that their average time studying is between 41 and 49 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.

Expert Solution

Step 1

We have given that a random variable X i.e, the amount of time is normally distributed with mean 45 minutes and standard deviation 20 minutes. The sample of size n is 7.