Answered: A recent personalized information sheet…

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 recent personalized information sheet from your wireless phone carrier claims that the mean duration of all your phone calls was μ=3.1 minutes with a standard deviation of σ=2.4 minutes. From a random sample of n=50 calls, your parents computed a sample mean of x=4.1 minutes and a sample standard deviation of s=3.2 minutes. Complete parts a through e below.

a. Sketch the population distribution for the duration of your phone calls. What are its mean and standard deviation?

b. What are the mean and standard deviation of the data distribution?

c. Find the mean and standard deviation of the sampling distribution of the sample mean.

d. Is the sample mean of 4.1 minutes unusually high? Find its z-score and comment.

e. Your parents told you that they will kick you off the plan when they find a sample mean larger than 4.2 minutes. How likely is this to happen?

P(x>4.2 minutes)= ?

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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