A Social Researcher wishes to determine wishes to determine the relative ranking
ID: 3219845 • Letter: A
Question
A Social Researcher wishes to determine wishes to determine the relative rankings of urban crimes within the United States. The mean crime rate for the US is 32.0 with a standard deviation of 10.56.
All questions are in reference to the overall US crime statistics.
a) What is the percentile ranking of a city with an average crime rate of 38.02?
b) What is the percentage of crimes that fall below a city with a crime rate of 14.86?
c) What percentage of crimes are above a city with a crime rate of 53.67?
d) What percentage of crimes fall between 19.70 and 28.40?
e) What percentage of crimes fall between 19.70 and 68.71?
f) What is the z-score of a city that is at the 45th percentile?
g) What is the crime rate of a city that has a z-score of 4?
Explanation / Answer
given mean = 32
standard deviation = 10.56
a) What is the percentile ranking of a city with an average crime rate of 38.02?
we know z formulea = average - mean / standard devaiation
= (38.02-32) / 10.56
=0.5700
p(z) = 0.5700 looking from standard z table 0.7157= 1-0.7157=0.2843 = 28.43%
b) What is the percentage of crimes that fall below a city with a crime rate of 14.86?
we know z formulea = average - mean / standard devaiation
= (14.86-32) / 10.56
=-1.6231
looking this value in standard z table we have = 0.526=1-0.526= 0.474= 47.4%
c) What percentage of crimes are above a city with a crime rate of 53.67
we know z formulea = average - mean / standard devaiation
= (53.67-32) / 10.56
=2.052
now lookinf this value in z table = 0.9798
= 1-0.9798=0.0202= 2.02%
4) What percentage of crimes fall between 19.70 and 28.40?
we know z formulea = average - mean / standard devaiation
z1= (19.70-32) / 10.56 =-1.164
z2= (68.71-32) / 10.56 =3.476
p(x<19.770<x>68.71) = 0.997-0.1230
=0.874= 1-0.874=0.126= 12.6%
f) What is the z-score of a city that is at the 45th percentile?
we know z formulea = average - mean / standard devaiation
z= (45-32) / 10.56 =1.2310
g) What is the crime rate of a city that has a z-score of 4?
we know z formulea = average - mean / standard devaiation
4 =x-32 / 10.56
42.24 = x -32
74.24 =x
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