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 isy = 0.185 +0.007x and that = 0.005. Then, for a fixed x value, y has a normal distribution with mean 0.185 +0.007x and standard deviation 0.005.USE SALT(a) What is the mean eggshell thickness for quail eggs that are 15 mm in length?μmWhat 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 0.29 um?(c) Approximately what proportion of quail eggs of length 14 mm have a shell thickness of greater than 0.282? (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 0.286? (Round your answer to four decimal places.)

Given:- y = 0.185 +0.007x and that sigma= 0.005.

Answered: he mean eggshell thickness for quail…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
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