What is the Normal Distribution of X in Vehicle Speed Observation?

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Homework Help Overview

The discussion revolves around the normal distribution of a variable X, which represents the speed of variation of the angle subtended by the width of a vehicle as observed by a driver. The original poster expresses uncertainty about how to approach the problem, which involves interpreting measurements related to vehicle speed and their distribution characteristics.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the concept of converting measurements to Z values for analysis and question the appropriate standard deviation to use in this context. There is also a focus on determining the fraction of measurements that exceed a certain threshold.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the problem setup and the correct interpretation of parameters. Some guidance has been offered regarding the conversion to Z values, but there is still uncertainty about the standard deviation to apply.

Contextual Notes

There is a lack of clarity regarding the specific problem statement and the definitions of the parameters involved, particularly the standard deviation in relation to the units of measurement.

csmumfau
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a vehicle driver gauges the relative speed of the next vehicle ahead by observing the speed with which the image of the width of that vehicle varies. This speed is proportional to X, the speed of variation of the angle at which the eye subtends this width. According to P. Ferrani and others, a study of many drivers revealed X to be normal distributed with a mean of 0 and a standard deviation of 10 ( [tex]10^{-4}[/tex] radians per sec)

I have no idea how to start, sorry.
 
Last edited:
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csmumfau said:
I have no idea how to start, sorry.

You haven't stated any problem or question.
 
Stephen Tashi said:
You haven't stated any problem or question.

My apologizes.

What fraction of these measurements is more than 5 units away from 0?
 
Have you studied how to rescale the units in problem by converting them to "Z values"? Convert +5 and-5 to Z values by using the scaling. For 5, Z = (5 - mean)/ (standard deviation)
 
Stephen Tashi said:
Have you studied how to rescale the units in problem by converting them to "Z values"? Convert +5 and-5 to Z values by using the scaling. For 5, Z = (5 - mean)/ (standard deviation)

Yeah, I know that but was is sigma? 10 or 10^{-4}
 
csmumfau said:
Yeah, I know that but was is sigma? 10 or 10^{-4}

I'd say it's 10 since the problem asks for "units" and not "radians per second".
 

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