A paper suggests that the simple linear regression model is reasonable for describing the relationship between y = eggshell thickness (in micrometers, μm) and x = egg length (mm) for quail eggs. Suppose that the population regression line is y = 0.165 +0.007x and that = 0.005. Then, for a fixed x value, y has a normal distribution with mean 0.165 +0.007x and standard deviation 0.005. (a) What is the mean eggshell thickness for quail eggs that are 15 mm in length? um What is the mean eggshell thickness for quail eggs that are 17 mm in length? um (b) What is the probability that a quail egg with a length of 15 mm will have a shell thickness that is greater than 0.27 μm? (c) Approximately what proportion of quail eggs of length 14 mm have a shell thickness of greater than 0.26? (Hint: The distribution of y at a fixed x is approximately normal. Round your answer to four decimal places.) Approximately what proportion of quail eggs of length 14 mm have a shell thickness of less than 0.265? (Round your answer to four decimal places.)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
A paper suggests that the simple linear regression model is reasonable for describing the relationship between y = eggshell thickness (in
micrometers, μm) and x = egg length (mm) for quail eggs. Suppose that the population regression line is y = 0.165 +0.007x and that o
%e = 0.005.
Then, for a fixed x value, y has a normal distribution with mean 0.165 + 0.007x and standard deviation 0.005.
(a) What is the mean eggshell thickness for quail eggs that are 15 mm in length?
μm
What is the mean eggshell thickness for quail eggs that are 17 mm in length?
μm
(b) What is the probability that a quail egg with a length of 15 mm will have a shell thickness that is greater than 0.27 μm?
(c) Approximately what proportion of quail eggs of length 14 mm have a shell thickness of greater than 0.26? (Hint: The distribution of y at a
fixed x is approximately normal. Round your answer to four decimal places.)
Approximately what proportion of quail eggs of length 14 mm have a shell thickness of less than 0.265? (Round your answer to four decimal
places.)
Transcribed Image Text:A paper suggests that the simple linear regression model is reasonable for describing the relationship between y = eggshell thickness (in micrometers, μm) and x = egg length (mm) for quail eggs. Suppose that the population regression line is y = 0.165 +0.007x and that o %e = 0.005. Then, for a fixed x value, y has a normal distribution with mean 0.165 + 0.007x and standard deviation 0.005. (a) What is the mean eggshell thickness for quail eggs that are 15 mm in length? μm What is the mean eggshell thickness for quail eggs that are 17 mm in length? μm (b) What is the probability that a quail egg with a length of 15 mm will have a shell thickness that is greater than 0.27 μm? (c) Approximately what proportion of quail eggs of length 14 mm have a shell thickness of greater than 0.26? (Hint: The distribution of y at a fixed x is approximately normal. Round your answer to four decimal places.) Approximately what proportion of quail eggs of length 14 mm have a shell thickness of less than 0.265? (Round your answer to four decimal places.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman