You may need to use the appropriate appendix table or technology to answer this question. The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 35 years of rainfall for California and a sample of 46 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. inches ^^ ^^ 10 14 18 22 26 30 34 inches 39.9 40.6 41.3 42 42.7 43.4 44.1 19.9 20.6 21.3 22 22.7 23.4 24.1 -2.1-1.4 -0.7 0.7 1.4 2.1 part (c), because the sample size is larger O part (c), because the population standard deviation is smaller O part (b), because the standard error is smaller O part (b), because the population standard deviation is smaller inches inches (b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.) 0.8614 x (c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.) 0.6222 x (d) In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?
You may need to use the appropriate appendix table or technology to answer this question. The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 35 years of rainfall for California and a sample of 46 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. inches ^^ ^^ 10 14 18 22 26 30 34 inches 39.9 40.6 41.3 42 42.7 43.4 44.1 19.9 20.6 21.3 22 22.7 23.4 24.1 -2.1-1.4 -0.7 0.7 1.4 2.1 part (c), because the sample size is larger O part (c), because the population standard deviation is smaller O part (b), because the standard error is smaller O part (b), because the population standard deviation is smaller inches inches (b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.) 0.8614 x (c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.) 0.6222 x (d) In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?
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
Transcribed Image Text:You may need to use the appropriate appendix table or technology to answer this question.
The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation
for both states is 4 inches. A sample of 35 years of rainfall for California and a sample of 46 years of rainfall for New York has been taken.
(a) Show the probability distribution of the sample mean annual rainfall for California.
^^
inches
39.9 40.6 41.3 42 42.7 43.4 44.1
19.9 20.6 21.3 22 22.7 23.4 24.1
inches
-2.1 -1.4 -0.7
0 0.7 1.4 2.1
10 14 18 22 26
part (c), because the sample size is larger
part (c), because the population standard deviation is smaller
part (b), because the standard error is smaller
O part (b), because the population standard deviation is smaller
30
34
inches
inches
(b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.)
0.8614
x
(c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)
0.6222.
x
(d) In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?
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 5 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