Answered: 1. Say that you will have to wait for a…

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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A. Solve the following. Show your complete solution.

1. Say that you will have to wait for a bus. Assume that the amount of waiting time is normally distributed between 0 and 15 minutes. Suppose that the mean time of a person is 8 minutes and the standard deviation is 1.8. What is the probability that you will wait for less than 12.5 minutes?

2. The length of time between charges of the battery of laptops is normally distributed with a mean of 45 hours and a standard deviation of 12 hours. Fiel owns one of these laptops and wants to know the probability that the length of time will be between 50 and 70 hours.

3. The length of life of an ordinary flashlight produced by a company has a normal distribution with a mean of 36 months and a standard deviation of 5 months. Find the probability that the flashlight produced by the company will last (a) more than 18 months, (b) between 17 and 32 months.

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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