Answered: Daily observations for a period of 144…

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

Daily observations for a period of 144 days have been conducted about the
number of candy bars sold from a vending machine. Using these observations, the
sample mean is calculated to be 258 and the sample standard deviation is calculated
to be 60.
a.) What is the probability that the sample mean number of candy bars
sold for the 144-day period is less than 273?
b.) What is the probability that the total number of candy bars sold for
the 144-day period is greater than 34,992 but less than 37,872?
(c) If the profit per candy bar is 5 cents, what is the probability that the
average profit per day over the 144-day period is at least $12.65?

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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