Reaction time is the amount of time it takes to respond to a stimulus, and for automobile drivers, it is an important factor in staying safe while on the road by avoiding rear-end collisions. Reaction times vary from driver to driver and tend to be longer than one might think. A recent study determined that the time for an in-traffic driver to react to a brake signal from standard brake lights can be modeled with a normal distribution having mean value 1.24 seconds and standard deviation of 0.45 seconds. If we let X denote reaction time for automobile drivers, use the appropriate Normal Distribution to determine each of the following. 1. What is the probability that a driver has a reaction time less than 0.6 seconds? 2. Approximately what proportion of drivers have a reaction time more than 2.5 seconds? 3. Within what limits, centered about the mean, would you expect driver reaction times to lie with 95% probability ? What are the z-scores for these limits? 4. What is the reaction time for which only 1% of drivers have a shorter reaction time? What is its z-score? 5. What is the reaction time for which only about 5% of drivers have a longer reaction time? What is its z-score? 6. Approximately what proportion of drivers have a reaction time within three standard deviations of the mean?
Reaction time is the amount of time it takes to respond to a stimulus, and for automobile drivers, it is an important factor in staying safe while on the road by avoiding rear-end collisions. Reaction times vary from driver to driver and tend to be longer than one might think. A recent study determined that the time for an in-traffic driver to react to a brake signal from standard brake lights can be modeled with a normal distribution having mean value 1.24 seconds and standard deviation of 0.45 seconds. If we let X denote reaction time for automobile drivers, use the appropriate Normal Distribution to determine each of the following. 1. What is the probability that a driver has a reaction time less than 0.6 seconds? 2. Approximately what proportion of drivers have a reaction time more than 2.5 seconds? 3. Within what limits, centered about the mean, would you expect driver reaction times to lie with 95% probability ? What are the z-scores for these limits? 4. What is the reaction time for which only 1% of drivers have a shorter reaction time? What is its z-score? 5. What is the reaction time for which only about 5% of drivers have a longer reaction time? What is its z-score? 6. Approximately what proportion of drivers have a reaction time within three standard deviations of the mean?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Reaction time is the amount of time it takes to respond to a stimulus, and for automobile drivers, it is an important factor in staying safe while on the road by avoiding rear-end collisions. Reaction times vary
from driver to driver and tend to be longer than one might think. A recent study determined that the time for an in-traffic driver to react to a brake signal from standard brake lights can be modeled with a
normal distribution having mean value 1.24 seconds and standard deviation of 0.45 seconds.
If we let X denote reaction time for automobile drivers, use the appropriate Normal Distribution to determine each of the following.
1. What is the probability that a driver has a reaction time less than 0.6 seconds?
2. Approximately what proportion of drivers have a reaction time more than 2.5 seconds?
3. Within what limits, centered about the mean, would you expect driver reaction times to lie with 95% probability? What are the z-scores for these limits?
4. What is the reaction time for which only 1% of drivers have a shorter reaction time? What is its z-score?
5. What is the reaction time for which only about 5% of drivers have a longer reaction time? What is its z-score?
6. Approximately what proportion of drivers have a reaction time within three standard deviations of the mean?
Transcribed Image Text:(a) To model the random variable X defined by the selected scenario, use the Normal Distribution with mean
(b) Determine each of the following values, rounded to four decimal places.
1.
2.
3. The smaller value is
The larger value is
4. X =
6.
Z-score =
5. X =
Z-score =
with a corresponding z-score of
with a corresponding z-score of
and standard deviation
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