(c) What is the probability of obtaining x = 66 or fewer individuals with the characteristic? That is, what is P(ps0.33)? POs0.33) = (Round to four decimal places as needed.)
(c) What is the probability of obtaining x = 66 or fewer individuals with the characteristic? That is, what is P(ps0.33)? POs0.33) = (Round to four decimal places as needed.)
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
Question
P(p<0.33)
![Suppose a simple random sample of size \( n = 200 \) is obtained from a population whose size is \( N = 20,000 \) and whose population proportion with a specified characteristic is \( p = 0.4 \). Complete parts (a) through (c) below.
- Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \).
- Not normal because \( n > 0.05N \) and \( np(1 - p) < 10 \).
- Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \).
Determine the mean of the sampling distribution of \( \hat{p} \).
\[ \mu_{\hat{p}} = p = 0.4 \] (Round to one decimal place as needed.)
Determine the standard deviation of the sampling distribution of \( \hat{p} \).
\[ \sigma_{\hat{p}} = 0.034641 \] (Round to six decimal places as needed.)
(b) What is the probability of obtaining \( x \geq 90 \) or more individuals with the characteristic? That is, what is \( P(\hat{p} \geq 0.45) \)?
\[ P(\hat{p} \geq 0.45) = 0.0745 \] (Round to four decimal places as needed.)
(c) What is the probability of obtaining \( x \leq 66 \) or fewer individuals with the characteristic? That is, what is \( P(\hat{p} \leq 0.33) \)?
\[ P(\hat{p} \leq 0.33) = 0.0339 \] (Round to four decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca98936e-33c7-4402-95ae-aeafe8e3f8b8%2Ff919a487-3d84-4872-bd39-f1cb218072eb%2F0ydpoqe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose a simple random sample of size \( n = 200 \) is obtained from a population whose size is \( N = 20,000 \) and whose population proportion with a specified characteristic is \( p = 0.4 \). Complete parts (a) through (c) below.
- Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \).
- Not normal because \( n > 0.05N \) and \( np(1 - p) < 10 \).
- Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \).
Determine the mean of the sampling distribution of \( \hat{p} \).
\[ \mu_{\hat{p}} = p = 0.4 \] (Round to one decimal place as needed.)
Determine the standard deviation of the sampling distribution of \( \hat{p} \).
\[ \sigma_{\hat{p}} = 0.034641 \] (Round to six decimal places as needed.)
(b) What is the probability of obtaining \( x \geq 90 \) or more individuals with the characteristic? That is, what is \( P(\hat{p} \geq 0.45) \)?
\[ P(\hat{p} \geq 0.45) = 0.0745 \] (Round to four decimal places as needed.)
(c) What is the probability of obtaining \( x \leq 66 \) or fewer individuals with the characteristic? That is, what is \( P(\hat{p} \leq 0.33) \)?
\[ P(\hat{p} \leq 0.33) = 0.0339 \] (Round to four decimal places as needed.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman