Answered: Furnace repair bills are normally…

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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If we were to define an event as being unusual if it occurs less than 5% of the time, would we consider a sample of size n=36 that had a sample mean of 87kg to be considered unusual? Why or why not?

Furnace repair bills are normally distributed with a mean of µ = 273 dollars and a standard deviation of σ = 25 dollars. If n = 100 of these repair bills are randomly selected, find the probability that they have a mean cost, , between 270 dollars and 276 dollars. i.e. find P(270 < < 276). In calculating the z-score, round your z-score to two decimal places. Use the normal table to find the probability and give answer to 4 decimal places.

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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If we were to define an event as being unusual if it occurs less than 5% of the time, would we consider a sample of size n=36 that had a sample mean of 87kg to be considered unusual? Why or why not? (hint: number 6 gives the 95th percentile).

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