Answered: The amount of time devoted to studying…

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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The amount of time devoted to studying statistics each week by students who achieve a grade of A in the course is a normally distributed random variable, with a mean of 7.5 hours and a standard deviation of 2.1 hours. Also indicate whether the event is usual or unusual

A. What proportion of A students study more than 10 hours per week

B. Find the probability that an A student spends between 7 and 9 hours studying

C. What proportion of A students spend fewer than 3 hours studying

*Please do not solve using Microsoft Excel. My professor is not teaching using excel. I would like to see the steps involved to solving the problem for my own study reference for exams.*

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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The amount of time devoted to preparing for a statistics examination by students is a normally distributed random variable with a mean of 17 hours and a standard deviation of 5 hours. Required:

d) What is the probability that a student spends at least 15 hours studying?
e) What is the probability that a student spends at most 18 hours studying?

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