The Department of Transportation (DoT) is concerned about the high speed of vehicles traveling down a dangerous stretch of an interstate highway with a posted speed limit of 55 mph. Part I An extensive study has revealed that the speed of vehicles traveling down the dangerous stretch is normally distributed with a mean speed of 65.3 mph and a standard deviation of 6.8 mph. (a) What is the probability that a random vehicle travels at a speed in excess of 20 mph of the posted speed limit? (Round your answer to three decimal places.) (b) What is the probability that a random vehicle travels slower than 5 mph under the posted speed limit? (Round your answer to three decimal places.) (c) What is the probability that a random vehicle travels at a speed that is between the posted speed limit and 10 mph in excess of it? (Round your answer to three decimal places.) (d) What speed corresponds to the 90th percentile? (Round your answer to one decimal place.) mph Part II The Department of Transportation (DoT) collects the speeds of a random sample of 95 vehicles traveling down the dangerous stretch of highway. (e) How many of the 95 vehicles would the DoT expect to travel at a speed that is between the posted speed limit and 10 mph in excess of it? (Round your answer to the nearest integer.) vehicles (f) Show the sampling distribution of the sample mean speed. (g) What is the probability that the sample mean speed falls within 1 mph of the population mean? (Round your answer to three decimal place.) (h) What is the probability that the sample mean speed is in excess of 66.4 mph? (Round your answer to three decimal place.) Part III The Department of Transportation (DoT) decides to seek the help of state police, who respond by heavily patrolling the dangerous stretch of highway as a deterrent. When the DoT monitors again the speed of vehicles, it discovers that the speed distribution is still normal, but the mean speed has dropped to 55.3 mph, and the standard deviation to 3.4 mph. (i) What is now the probability that a random vehicle travels at a speed that is between the posted speed limit and 10 mph in excess of it? (Round your answer to three decimal place.) (j) Using the newly reduced mean speed and standard deviation, what speed now corresponds to the 90th percentile? (Round your answer to one decimal place.) mph (k) Using the newly reduced mean speed and standard deviation, how many of the 95 vehicles traveling down the dangerous stretch of highway would the DoT now expect to travel at a speed that is between the posted speed limit and 10 mph in excess of it? (Round your answer to the nearest integer.) vehicles

The Department of Transportation (DoT) is concerned about the high speed of vehicles traveling down a dangerous stretch of an interstate highway with a posted speed limit of 55 mph. Part I An extensive study has revealed that the speed of vehicles traveling down the dangerous stretch is normally distributed with a mean speed of 65.3 mph and a standard deviation of 6.8 mph. (a) What is the probability that a random vehicle travels at a speed in excess of 20 mph of the posted speed limit? (Round your answer to three decimal places.) (b) What is the probability that a random vehicle travels slower than 5 mph under the posted speed limit? (Round your answer to three decimal places.) (c) What is the probability that a random vehicle travels at a speed that is between the posted speed limit and 10 mph in excess of it? (Round your answer to three decimal places.) (d) What speed corresponds to the 90th percentile? (Round your answer to one decimal place.) mph Part II The Department of Transportation (DoT) collects the speeds of a random sample of 95 vehicles traveling down the dangerous stretch of highway. (e) How many of the 95 vehicles would the DoT expect to travel at a speed that is between the posted speed limit and 10 mph in excess of it? (Round your answer to the nearest integer.) vehicles (f) Show the sampling distribution of the sample mean speed. (g) What is the probability that the sample mean speed falls within 1 mph of the population mean? (Round your answer to three decimal place.) (h) What is the probability that the sample mean speed is in excess of 66.4 mph? (Round your answer to three decimal place.) Part III The Department of Transportation (DoT) decides to seek the help of state police, who respond by heavily patrolling the dangerous stretch of highway as a deterrent. When the DoT monitors again the speed of vehicles, it discovers that the speed distribution is still normal, but the mean speed has dropped to 55.3 mph, and the standard deviation to 3.4 mph. (i) What is now the probability that a random vehicle travels at a speed that is between the posted speed limit and 10 mph in excess of it? (Round your answer to three decimal place.) (j) Using the newly reduced mean speed and standard deviation, what speed now corresponds to the 90th percentile? (Round your answer to one decimal place.) mph (k) Using the newly reduced mean speed and standard deviation, how many of the 95 vehicles traveling down the dangerous stretch of highway would the DoT now expect to travel at a speed that is between the posted speed limit and 10 mph in excess of it? (Round your answer to the nearest integer.) vehicles

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Related questions

Question

The Department of Transportation (DoT) is concerned about the high speed of vehicles traveling down a dangerous stretch of an interstate highway with a posted speed limit of 55 mph.

Part I

An extensive study has revealed that the speed of vehicles traveling down the dangerous stretch is normally distributed with a mean speed of 65.3 mph and a standard deviation of 6.8 mph.

(a)

What is the probability that a random vehicle travels at a speed in excess of 20 mph of the posted speed limit? (Round your answer to three decimal places.)

(b)

What is the probability that a random vehicle travels slower than 5 mph under the posted speed limit? (Round your answer to three decimal places.)

(c)

What is the probability that a random vehicle travels at a speed that is between the posted speed limit and 10 mph in excess of it? (Round your answer to three decimal places.)

(d)

What speed corresponds to the 90th percentile? (Round your answer to one decimal place.)

mph

Part II

The Department of Transportation (DoT) collects the speeds of a random sample of 95 vehicles traveling down the dangerous stretch of highway.

(e)

How many of the 95 vehicles would the DoT expect to travel at a speed that is between the posted speed limit and 10 mph in excess of it? (Round your answer to the nearest integer.)

vehicles

(f)

Show the sampling distribution of the sample mean speed.

(g)

What is the probability that the sample mean speed falls within 1 mph of the population mean? (Round your answer to three decimal place.)

(h)

What is the probability that the sample mean speed is in excess of 66.4 mph? (Round your answer to three decimal place.)

Part III

The Department of Transportation (DoT) decides to seek the help of state police, who respond by heavily patrolling the dangerous stretch of highway as a deterrent. When the DoT monitors again the speed of vehicles, it discovers that the speed distribution is still normal, but the mean speed has dropped to 55.3 mph, and the standard deviation to 3.4 mph.

(i)

What is now the probability that a random vehicle travels at a speed that is between the posted speed limit and 10 mph in excess of it? (Round your answer to three decimal place.)

(j)

Using the newly reduced mean speed and standard deviation, what speed now corresponds to the 90th percentile? (Round your answer to one decimal place.)

mph

(k)

Using the newly reduced mean speed and standard deviation, how many of the 95 vehicles traveling down the dangerous stretch of highway would the DoT now expect to travel at a speed that is between the posted speed limit and 10 mph in excess of it? (Round your answer to the nearest integer.)

vehicles

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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