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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
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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**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.
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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