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Vehicle speed on a particular bridge in China can be modeled as normally distributed. USE SALT (a) If 5% of all vehicles travel less than 39.18 m/h and 10 % travel more than 73.24 m/h, what are the mean and standard deviation of vehicle speed? (Round your answers to three decimal places.) mean 20.7891 11.617 standard deviation (b) What is the probability that a randomly selected vehicle's speed is between 50 and 65 m/h? (Round your answer to four decimal places.) 0.006 x (c) What is the probability that a randomly selected vehicle's speed exceeds the speed limit of 70 m/h? (Round your answer to four decimal places.) X 0.00001

Vehicle speed on a particular bridge in China can be modeled as normally distributed. USE SALT (a) If 5% of all vehicles travel less than 39.18 m/h and 10 % travel more than 73.24 m/h, what are the mean and standard deviation of vehicle speed? (Round your answers to three decimal places.) mean 20.7891 11.617 standard deviation (b) What is the probability that a randomly selected vehicle's speed is between 50 and 65 m/h? (Round your answer to four decimal places.) 0.006 x (c) What is the probability that a randomly selected vehicle's speed exceeds the speed limit of 70 m/h? (Round your answer to four decimal places.) X 0.00001

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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## Normal Distribution of Vehicle Speed on a Bridge in China Vehicle speeds on a specific bridge in China follow a normal distribution. ### Problems and Solutions #### (a) **Problem:** If 5% of all vehicles travel at speeds less than 39.18 m/h and 10% exceed 73.24 m/h, determine the mean and standard deviation of vehicle speed. (Round your answers to three decimal places.) - **Mean:** - Calculated as **20.7891** (incorrect) - **Standard Deviation:** - Calculated as **11.817** (correct) #### (b) **Problem:** What is the probability that a randomly selected vehicle travels between 50 and 65 m/h? (Round your answer to four decimal places.) - **Probability:** - Calculated as **0.008** (incorrect) #### (c) **Problem:** What is the probability that a randomly selected vehicle exceeds the speed limit of 70 m/h? (Round your answer to four decimal places.) - **Probability:** - Calculated as **0.0001** (incorrect) ### Explanation In these cases involving normal distribution, a common approach would be to use statistical tools or tables to determine the probabilities based on the given parameters. The normal distribution is defined by the mean and standard deviation, which dictate the shape and spread of the distribution curve.
Transcribed Image Text:## Normal Distribution of Vehicle Speed on a Bridge in China Vehicle speeds on a specific bridge in China follow a normal distribution. ### Problems and Solutions #### (a) **Problem:** If 5% of all vehicles travel at speeds less than 39.18 m/h and 10% exceed 73.24 m/h, determine the mean and standard deviation of vehicle speed. (Round your answers to three decimal places.) - **Mean:** - Calculated as **20.7891** (incorrect) - **Standard Deviation:** - Calculated as **11.817** (correct) #### (b) **Problem:** What is the probability that a randomly selected vehicle travels between 50 and 65 m/h? (Round your answer to four decimal places.) - **Probability:** - Calculated as **0.008** (incorrect) #### (c) **Problem:** What is the probability that a randomly selected vehicle exceeds the speed limit of 70 m/h? (Round your answer to four decimal places.) - **Probability:** - Calculated as **0.0001** (incorrect) ### Explanation In these cases involving normal distribution, a common approach would be to use statistical tools or tables to determine the probabilities based on the given parameters. The normal distribution is defined by the mean and standard deviation, which dictate the shape and spread of the distribution curve.
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