# Educational Content: Sampling Distribution of p## Exercise 07.31 Algo (Sampling Distribution of p)### ContextThe president of Doerman Distributors, Inc., believes that 32% of the firm's orders come from first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of first-time customers.### Problem Statements1. **Assumptions and Distribution** - Assume the president’s belief is correct with \( p = 0.32 \). - **Question:** What is the sampling distribution of \( \hat{p} \) for this study? - **Answer:** It's a normal distribution because \( np \) and \( n(1-p) \) are both greater than 5. ✔️2. **Probability Calculations** - **Question (b):** What is the probability that the sample proportion will be between 0.24 and 0.40 (to 4 decimals)? - **Answer:** 0.9146 ✔️ - **Question (c):** What is the probability that the sample proportion will be between 0.29 and 0.35 (to 4 decimals)? - **Answer Section:** Incorrect attempt with a blank input. ❌### Feedback- **Status:** Partially Correct- **Action:** The student may review their calculations for the latter probability question, ensuring the correct use of the z-table for precise results.#### NoteThe exercise is part of a statistical estimate on sampling distributions, emphasizing the importance of normal distribution assumptions and probability calculations using z-tables.## Additional Resources- Z-table lookup and application- Concepts of normal distribution and sampling proportions### Technical Details- This task was performed on a MacBook Pro, using browser-based educational software (Cengage MindTap). - Comments and progress are tracked, providing immediate student feedback and opportunities for iterative learning.

Given: Population proportion = P = 32% = 0.32 Sample size = n = 100

The president of Doerman Distributors, Inc., believes that 32% of the firm's orders come from first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of first-time customers. Use z-table. a. Assume that the president is correct and p = 0.32. What is the sampling distribution of p for this study? A normal distribution because np and n(1-p) are both greater than 5 b. What is the probability that the sample proportion will be between 0.24 and 0.40 (to 4 decimals)? .9146 c. What is the probability that the sample proportion will be between 0.29 and 0.35 (to 4 decimals)?

The president of Doerman Distributors, Inc., believes that 32% of the firm's orders come from first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of first-time customers. Use z-table. a. Assume that the president is correct and p = 0.32. What is the sampling distribution of p for this study? A normal distribution because np and n(1-p) are both greater than 5 b. What is the probability that the sample proportion will be between 0.24 and 0.40 (to 4 decimals)? .9146 c. What is the probability that the sample proportion will be between 0.29 and 0.35 (to 4 decimals)?

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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