5. A realtor is studying the probability that 5 houses will sell the first week they are listed for sale out of 20 houses that are first listed for sale this week. The current probability of a house selling the week is is listed is 43%. Use this question to answer each part below. a. Define success for THIS problem. b. Find n, x, p, q X= P= q= c. What is the standard deviation for this problem? Answer with 2-places past the decimal.
5. A realtor is studying the probability that 5 houses will sell the first week they are listed for sale out of 20 houses that are first listed for sale this week. The current probability of a house selling the week is is listed is 43%. Use this question to answer each part below. a. Define success for THIS problem. b. Find n, x, p, q X= P= q= c. What is the standard deviation for this problem? Answer with 2-places past the decimal.
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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6.
![**Problem 6: Probability and Standard Deviation**
A realtor is studying the probability that 5 houses will sell in the first week they are listed for sale, out of 20 houses that are first listed for sale this week. The current probability of a house selling the week it is listed is 43%. Use this question to answer each part below.
a. **Define Success for THIS Problem:**
- Success is defined as a house selling in the first week it is listed for sale.
b. **Find n, x, p, q:**
- \( n = \) (Number of trials: the number of houses listed)
- \( x = \) (Number of successes: the number of houses sold in the first week)
- \( p = \) (Probability of success: current probability of selling a house in the first week)
- \( q = \) (Probability of failure: \( 1 - p \))
\[
\begin{align*}
n &= 20 \\
x &= 5 \\
p &= 0.43 \\
q &= 0.57 \\
\end{align*}
\]
c. **What is the Standard Deviation for this Problem? Answer with 2-Places Past the Decimal:**
- The standard deviation of a binomial distribution is calculated using the formula: \[ \sigma = \sqrt{n \cdot p \cdot q} \]
- Substitute the values found in part (b) to calculate the standard deviation.
d. **Write the FILLED-IN Formula Used to Solve this Probability Problem:**
- Use the binomial probability formula:
\[ P(X = x) = \binom{n}{x} \cdot p^x \cdot q^{(n-x)} \]
- Plug in the values for the current problem.
e. **Find the Probability Asked for with 3-Decimal Values or as a Percent with 1-Decimal:**
- Calculate the probability that exactly 5 houses sell in the first week using the formula from part (d).
- Express the probability as a decimal to three places or as a percentage to one decimal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bc92d6f-8141-453b-b1aa-15dddf73f72d%2F33d154bb-358e-4644-8dab-4c42d4249eb6%2F3b7vjpd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 6: Probability and Standard Deviation**
A realtor is studying the probability that 5 houses will sell in the first week they are listed for sale, out of 20 houses that are first listed for sale this week. The current probability of a house selling the week it is listed is 43%. Use this question to answer each part below.
a. **Define Success for THIS Problem:**
- Success is defined as a house selling in the first week it is listed for sale.
b. **Find n, x, p, q:**
- \( n = \) (Number of trials: the number of houses listed)
- \( x = \) (Number of successes: the number of houses sold in the first week)
- \( p = \) (Probability of success: current probability of selling a house in the first week)
- \( q = \) (Probability of failure: \( 1 - p \))
\[
\begin{align*}
n &= 20 \\
x &= 5 \\
p &= 0.43 \\
q &= 0.57 \\
\end{align*}
\]
c. **What is the Standard Deviation for this Problem? Answer with 2-Places Past the Decimal:**
- The standard deviation of a binomial distribution is calculated using the formula: \[ \sigma = \sqrt{n \cdot p \cdot q} \]
- Substitute the values found in part (b) to calculate the standard deviation.
d. **Write the FILLED-IN Formula Used to Solve this Probability Problem:**
- Use the binomial probability formula:
\[ P(X = x) = \binom{n}{x} \cdot p^x \cdot q^{(n-x)} \]
- Plug in the values for the current problem.
e. **Find the Probability Asked for with 3-Decimal Values or as a Percent with 1-Decimal:**
- Calculate the probability that exactly 5 houses sell in the first week using the formula from part (d).
- Express the probability as a decimal to three places or as a percentage to one decimal.
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