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Name: The manager of a computer retails store is concerned that his supplier
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Description: The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a m

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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The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.1 years and a standard deviation of 0.4 years. He then randomly selects records on 32 laptops sold in the past and finds that the mean replacement time is 3.9 years.

Assuming that the laptop replacement times have a mean of 4.1 years and a standard deviation of 0.4 years, find the probability that 32 randomly selected laptops will have a mean replacement time of 3.9 years or less.
P(M < 3.9 years) =
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Based on the result above, does it appear that the computer store has been given laptops of lower than average quality?

Yes. The probability of this data is unlikely to have occurred by chance alone.
No. The probability of obtaining this data is high enough to have been a chance occurrence.

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 + ...

Expert Solution

Step 1

GIven Information:

Population mean (u) = 4.1 years

Standard Deviation ( $σ$ ) =0.4 years

Sample mean (x) = 3.9 years

Sample size (n) = 32

To determine the probability, there is a need to determine the z score first.

$z = \frac{x - u}{\frac{σ}{\sqrt{n}}} = \frac{3.9 - 4.1}{\frac{0.4}{\sqrt{32}}} = - 2.82$ 8

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