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Assume the speed of vehicles along an open stretch of a certain highway in Texas that is not heavily traveled has an approximately Normal distribution with a mean of 71 mph and a standard deviation of 3.125 mph.

Assume the speed of vehicles along an open stretch of a certain highway in Texas that is not heavily traveled has an approximately Normal distribution with a mean of 71 mph and a standard deviation of 3.125 mph.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Please answer question 1, section d.

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**Educational Website Content: Analyzing Vehicle Speeds and IQ Distributions** --- ### Problem 1: Vehicle Speeds on a Texas Highway 1. Assume the speed of vehicles along an open stretch of a certain highway in Texas, which is not heavily traveled, follows an approximately Normal distribution with a mean (μ) of 71 mph and a standard deviation (σ) of 3.125 mph. (Make sure to show how you got your answers) **Questions:** a) **Current Speed Limit**: The current posted speed limit is 65 mph. What is the proportion of vehicles going above this limit? b) **Below 50 mph**: What proportion of the vehicles would be going less than 50 mph? c) **Between 60 and 75 mph**: What proportion of the vehicles would be going between 60 and 75 mph? d) **New Speed Limit Proposal**: State authorities acknowledge that the road is not heavily trafficked and can handle a higher speed limit. However, they will implement a high fee for speeding over the new speed limit to ensure safety. Assume the same Normal distribution of speeds continues into the future. What should be the new speed limit so that only about 10% of vehicles exceed this limit? Show all of your reasoning and work in answering this. --- ### Problem 2: IQ Scores Distribution 2. Assume that IQ scores follow a Normal distribution with a mean (μ) of 100 and a standard deviation (σ) of 16. Using our IQR rule for determining IQ score outliers, what IQ scores would establish the lower and upper fences for determining outliers? (Make sure to show how you got your answers) --- **Instructions for Educators**: Encourage students to demonstrate their understanding by using the properties of Normal distributions and the IQR method. Provide step-by-step solutions to ensure students grasp key concepts such as z-scores and the calculation of fences for identifying outliers.
Transcribed Image Text:**Educational Website Content: Analyzing Vehicle Speeds and IQ Distributions** --- ### Problem 1: Vehicle Speeds on a Texas Highway 1. Assume the speed of vehicles along an open stretch of a certain highway in Texas, which is not heavily traveled, follows an approximately Normal distribution with a mean (μ) of 71 mph and a standard deviation (σ) of 3.125 mph. (Make sure to show how you got your answers) **Questions:** a) **Current Speed Limit**: The current posted speed limit is 65 mph. What is the proportion of vehicles going above this limit? b) **Below 50 mph**: What proportion of the vehicles would be going less than 50 mph? c) **Between 60 and 75 mph**: What proportion of the vehicles would be going between 60 and 75 mph? d) **New Speed Limit Proposal**: State authorities acknowledge that the road is not heavily trafficked and can handle a higher speed limit. However, they will implement a high fee for speeding over the new speed limit to ensure safety. Assume the same Normal distribution of speeds continues into the future. What should be the new speed limit so that only about 10% of vehicles exceed this limit? Show all of your reasoning and work in answering this. --- ### Problem 2: IQ Scores Distribution 2. Assume that IQ scores follow a Normal distribution with a mean (μ) of 100 and a standard deviation (σ) of 16. Using our IQR rule for determining IQ score outliers, what IQ scores would establish the lower and upper fences for determining outliers? (Make sure to show how you got your answers) --- **Instructions for Educators**: Encourage students to demonstrate their understanding by using the properties of Normal distributions and the IQR method. Provide step-by-step solutions to ensure students grasp key concepts such as z-scores and the calculation of fences for identifying outliers.
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It is given that mean is 71 and standard deviation is 3.125.

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