Answered: (A.) The lifetimes of a certain brand…

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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1. (A.) The lifetimes of a certain brand of battery are normally distributed with mean of 100 hours and standard deviation of 5 hours. The 95th percentile of battery lifetimes is:

į. 1.645

ii. -1.645

iii. 108.23

iv. 91.775

(B.) The reaction time it takes a driver to react to the brake lights on a decelerating vehicle is normally distributed with mean of 1.3 seconds and standard deviation of 0.5 seconds. We wish to calculate the probability that the reaction time of a driver is between 1.00 and 1.90 seconds. The area under the standard normal curve is:

į. 0.3893

ii. 0.2743

iii. 0.6107

iv. 0.8849

(C.) A survey indicated that children between ages of 2 and 5 years watch on average 24 hours of TV per week. The number of hours of TV watching per week by this age group is normally distributed with a standard deviation of 3 hours. We wish to compute the probability that the average number of hours of TV watched by 25 of these children will be greater than 26 hours. The area under the standard normal curve is:

į. 0.9996

ii. 0.7486

iii. 0.0004

iv. 0.2514

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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