Answered: Slices of pizza for a certain brand of…

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

Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 66.4 grams and a standard deviation of 1.95 grams.

Round answers to three decimal places.

a) For samples of size 18 pizza slices, what is the standard deviation for the sampling distribution of the sample mean?

b) What is the probability of finding a random slice of pizza with a mass of less than 66 grams?

c) What is the probability of finding a 18 random slices of pizza with a mean mass of less than 66 grams?

d) What sample mean (for a sample of size 18) would represent the bottom 15% (the 15th percentile)? grams

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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