Question

Use the following information to answer the next ten questions. The data that follow are the square footage (in 1,000 feet squared) of 28 homes. $$\begin{array}{|c|c|c|c|c|c|c|}\hline 1.5 & {2.4} & {3.6} & {2.6} & {1.6} & {2.4} & {2.0} \\ \hline 3.5 & {2.5} & {1.8} & {2.4} & {2.5} & {3.5} & {4.0} \\ \hline 2.6 & {1.6} & {2.2} & {1.8} & {3.8} & {2.5} & {1.5} \\\hline {2.8}&{1.8} &{4.5}&{1.9} &{1.9}& {3.1}& {1.6}\\\hline\end{array}$$ $$\text{Table 5.4}$$ The sample mean $=2.50$ and the sample standard deviation $=0.8302.$ The distribution can be written as $X \sim U(1.5,4.5).$ What is $P(2 < x < 3) ?$

Name: Problem 21, Chapter 5: Introductory Statistics
Uploaded: 2020-02-14T22:52:14-08:00
Duration: 33 s
Channel: Tony Wilson

   Use the following information to answer the next ten questions. The data that follow are the square footage (in 1,000 feet squared) of 28 homes.
$$\begin{array}{|c|c|c|c|c|c|c|}\hline 1.5 & {2.4} & {3.6} & {2.6} & {1.6} & {2.4} & {2.0} \\ \hline 3.5 & {2.5} & {1.8} & {2.4} & {2.5} & {3.5} & {4.0} \\ \hline 2.6 & {1.6} & {2.2} & {1.8} & {3.8} & {2.5} & {1.5} \\\hline {2.8}&{1.8} &{4.5}&{1.9} &{1.9}& {3.1}& {1.6}\\\hline\end{array}$$
$$\text{Table 5.4}$$
The sample mean $=2.50$ and the sample standard deviation $=0.8302.$
The distribution can be written as $X \sim U(1.5,4.5).$
What is $P(2 < x < 3) ?$

Introductory Statistics

Barbara Illowsky,… 1st Edition

Chapter 5, Problem 21

Instant Answer

Solved by Expert Tony Wilson

02/14/2020

Step 1

5,4.5)$. This means that the probability density function (pdf) is constant between the interval [1.5, 4.5]. The height of this pdf is given by $1/(b-a)$ where $a$ and $b$ are the lower and upper limits of the interval. In this case, $a=1.5$ and $b=4.5$, so the Show more…

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Use the following information to answer the next ten questions. The data that follow are the square footage (in 1,000 feet squared) of 28 homes. $$\begin{array}{|c|c|c|c|c|c|c|}\hline 1.5 & {2.4} & {3.6} & {2.6} & {1.6} & {2.4} & {2.0} \\ \hline 3.5 & {2.5} & {1.8} & {2.4} & {2.5} & {3.5} & {4.0} \\ \hline 2.6 & {1.6} & {2.2} & {1.8} & {3.8} & {2.5} & {1.5} \\\hline {2.8}&{1.8} &{4.5}&{1.9} &{1.9}& {3.1}& {1.6}\\\hline\end{array}$$ $$\text{Table 5.4}$$ The sample mean $=2.50$ and the sample standard deviation $=0.8302.$ The distribution can be written as $X \sim U(1.5,4.5).$ What is $P(2 < x < 3) ?$

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Key Concepts

Uniform Distribution

A continuous probability distribution where every outcome in the specified interval is equally likely. The probability density function remains constant over the interval, making calculations straightforward, as the total area under the density function across the interval is one.

Interval Length Ratio Method

In a uniform distribution, the probability of an event occurring within a certain subinterval is determined by dividing the length of that subinterval by the total length of the distribution's interval. This method leverages the constant density property to simplify probability calculations.

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