VPD Response Times to Emergencies Reach 10-YearHigh(Howell, 2017)The amount of time it takes Vancouver police officers to respond to an emergency call such as a robbery or a burglary in progress is increasing year over year and Police Chief Adam Palmer predicts itwill not get any better until more officers are hired.The average response time for an emergency call has gone from eight minutes and 33 seconds in 2008 to nine minutes and 43 seconds in 2017. That increase of more than a minute was captured by thedepartment in data recorded between January and June of each year for the past decade. Assume that the “priority-one” response time for Vancouver police can be approximated with a normal model with a mean of 10 minutes and a standard deviation of 2.5minutes. What proportion of theresponse times are at least 8 minutes but at most 12 minutes? ii.What proportionof the response times are at most 9 minutes?iii.20% of the response times are longer than how many minutes?iv.Find the IQR of the response times. Suppose that another “major city” claimed that its police force response times followed a normal model with a mean of 8 minutes. What is the SD of this model if 95% of the response times were at most 12 minutes? Show all steps in your solution.

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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VPD Response Times to Emergencies Reach 10-YearHigh(Howell, 2017)The amount of time it takes Vancouver police officers to respond to an emergency call such as a robbery or a burglary in progress is increasing year over year and Police Chief Adam Palmer predicts itwill not get any better until more officers are hired.The average response time for an emergency call has gone from eight minutes and 33 seconds in 2008 to nine minutes and 43 seconds in 2017. That increase of more than a minute was captured by thedepartment in data recorded between January and June of each year for the past decade.

Assume that the “priority-one” response time for Vancouver police can be approximated with a normal model with a mean of 10 minutes and a standard deviation of 2.5minutes.

What proportion of theresponse times are at least 8 minutes but at most 12 minutes?

ii.What proportionof the response times are at most 9 minutes?iii.20% of the response times are longer than how many minutes?iv.Find the IQR of the response times.

Suppose that another “major city” claimed that its police force response times followed a normal model with a mean of 8 minutes. What is the SD of this model if 95% of the response times were at most 12 minutes?

Show all steps in your solution.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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