sampling distribution of p se that best describes the shape of the sampling distribution below al because n≤0 05N and np(1-p) < 10 ately normal because n ≤0.05N and np(1-p) < 10 ately normal because n≤0.05N and np(1-p) > 10 al because n ≤0.05N and np(1-p) z 10. ean of the sampling distribution of p o one decimal place as needed.) andard deviation of the sampling distribution of p. o six decimal places as needed) obability of obtaining x= 18 or more individuals with the characteristic? That is what is P2024? Round to four decimal places as needed) obability of obtaining x-9 or fewer individuals with the characteristic? That is, what is P(p ≤0.12)?
sampling distribution of p se that best describes the shape of the sampling distribution below al because n≤0 05N and np(1-p) < 10 ately normal because n ≤0.05N and np(1-p) < 10 ately normal because n≤0.05N and np(1-p) > 10 al because n ≤0.05N and np(1-p) z 10. ean of the sampling distribution of p o one decimal place as needed.) andard deviation of the sampling distribution of p. o six decimal places as needed) obability of obtaining x= 18 or more individuals with the characteristic? That is what is P2024? Round to four decimal places as needed) obability of obtaining x-9 or fewer individuals with the characteristic? That is, what is P(p ≤0.12)?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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I need help with A through C. Thank you.
![**Sampling Distribution and Probability Calculations**
Suppose a simple random sample of size \( n = 75 \) is obtained from a population whose size is \( N = 10,000 \) and whose population proportion with a specified characteristic is \( p = 0.2 \). Complete parts (a) through (c) below.
### (a) Describe the sampling distribution of \(\hat{p}\)
Choose the phrase that best describes the shape of the sampling distribution below:
- **A.** Not normal because \( n \ge 0.05N \) and \( np(1 - p) < 10 \)
- **B.** Approximately normal because \( n < 0.05N \) and \( np(1 - p) < 10 \)
- **C.** Approximately normal because \( n \le 0.05N \) and \( np(1 - p) \ge 10 \)
- **D.** Not normal because \( n \le 0.05N \) and \( np(1 - p) \ge 10 \)
**Determine the mean of the sampling distribution of \(\hat{p}\):**
\[
\mu_{\hat{p}} = \boxed{}\ \ \ (Round to one decimal place as needed.)
\]
**Determine the standard deviation of the sampling distribution of \(\hat{p}\):**
\[
\sigma_{\hat{p}} = \boxed{}\ \ \ (Round to six decimal places as needed.)
\]
### (b) What is the probability of obtaining \( x = 18 \) or more individuals with the characteristic? That is, what is \( P(\hat{p} \ge 0.24) \)?
\[
P(\hat{p} \ge 0.24) = \boxed{}\ \ \ (Round to four decimal places as needed.)
\]
### (c) What is the probability of obtaining \( x = 9 \) or fewer individuals with the characteristic? That is, what is \( P(\hat{p} \le 0.12) \)?
\[
P(\hat{p} \le 0.12) = \boxed{}\ \ \ (Round to four decimal places as needed.)
\]
### Explanation of Graphs or Diagrams
There are no graphs or diagrams in this context to describe. The questions provided are theoretical and involve calculations based on](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F254f01d1-5636-4aee-8bdd-3770d49eb7a5%2F80cc312a-b785-4608-9629-0dddcae0b239%2F9xeet2b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Sampling Distribution and Probability Calculations**
Suppose a simple random sample of size \( n = 75 \) is obtained from a population whose size is \( N = 10,000 \) and whose population proportion with a specified characteristic is \( p = 0.2 \). Complete parts (a) through (c) below.
### (a) Describe the sampling distribution of \(\hat{p}\)
Choose the phrase that best describes the shape of the sampling distribution below:
- **A.** Not normal because \( n \ge 0.05N \) and \( np(1 - p) < 10 \)
- **B.** Approximately normal because \( n < 0.05N \) and \( np(1 - p) < 10 \)
- **C.** Approximately normal because \( n \le 0.05N \) and \( np(1 - p) \ge 10 \)
- **D.** Not normal because \( n \le 0.05N \) and \( np(1 - p) \ge 10 \)
**Determine the mean of the sampling distribution of \(\hat{p}\):**
\[
\mu_{\hat{p}} = \boxed{}\ \ \ (Round to one decimal place as needed.)
\]
**Determine the standard deviation of the sampling distribution of \(\hat{p}\):**
\[
\sigma_{\hat{p}} = \boxed{}\ \ \ (Round to six decimal places as needed.)
\]
### (b) What is the probability of obtaining \( x = 18 \) or more individuals with the characteristic? That is, what is \( P(\hat{p} \ge 0.24) \)?
\[
P(\hat{p} \ge 0.24) = \boxed{}\ \ \ (Round to four decimal places as needed.)
\]
### (c) What is the probability of obtaining \( x = 9 \) or fewer individuals with the characteristic? That is, what is \( P(\hat{p} \le 0.12) \)?
\[
P(\hat{p} \le 0.12) = \boxed{}\ \ \ (Round to four decimal places as needed.)
\]
### Explanation of Graphs or Diagrams
There are no graphs or diagrams in this context to describe. The questions provided are theoretical and involve calculations based on
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