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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 report announced that the median sales price of new houses sold one year was $211,000, and the mean sales price was $271,600. Assume that the standard deviation of the prices is $80,000.

If you select a random sample of n=100, what is the probability that the sample mean will be less than $300,000?

The probability that the sample mean will be less than $300,000 is__.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

Expert Solution

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According to the sum, A report announced that the median sales price of new houses sold one year was $211,000, and the mean sales price was $271,600. It is assumed that the standard deviation of the prices is $80,000.

Let X be a random variable that follows a normal distribution with mean $μ$ and variance $σ^{2}$ .

Here, $μ = 271, 600 a n d σ = 80, 000$

So, X $~ N (271600, 80000^{2})$

A random sample of n=100 is selected.

Thus the sample mean follows Normal distribution with mean $μ$ and variance $\frac{σ^{2}}{n}$

$X ~ N (271600, \frac{80000^{2}}{100})$

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