1 Blood alcohol concentrations of drivers involved in fatal

1. Blood alcohol concentrations of drivers involved in fatal crashes & then given jail sentencs are listed below. Find the range & standard deviation.

0.25 0.18 0.18 0.16 0.13 0.23

0.31 0.23 0.14 0.16 0.11 0.16

Find the range R=______

Find the standard deviation S=______ (round to the nearest thousandth as needed)

2. Statistics students particiapted in an experiment to test their ability to determine when 1 min(60 secs) has passed. The results are given below in seconds. Find the range & standard deviation for the given sample data.

Range=________sec

sample standard deviation________sec (round to the nearest tenth as needed)

3. IQ scores are normally distributed w/a mean of 100 & standard deviation of 15 assume that many samples of size n are taken from a large population of people & the mean IQ score is computed for each sample.

A. If the sample size is n=49, find the mean & standard deviation of the distribution of sample mean.

-The mean of the distribution of sample mean is _______

-The standard deviation of the distribution of sample means is _______(*same as below)

B. If the sample size is n=169 find the mean & standard deviation of the distribution of sample means.

-The mean of the distribution of sample means is_____

-The standard deviation of the distribution of sample means is _____ (type an integer or decimal rounded to the nearest tenth as needed)

Solution

The range is

range = max - min = 0.31 - 0.11 = 0.20 [ANSWER]

Getting the mean, X,              
              
X = Sum(x) / n              
Sum(x) =    2.24          
              
Thus,              
X =    0.186666667          
              
Setting up tables,              
x   x - X   (x - X)^2      
0.25   0.063333333   0.004011111      
0.18   -0.006666667   4.44444E-05      
0.18   -0.006666667   4.44444E-05      
0.16   -0.026666667   0.000711111      
0.13   -0.056666667   0.003211111      
0.23   0.043333333   0.001877778      
0.31   0.123333333   0.015211111      
0.23   0.043333333   0.001877778      
0.14   -0.046666667   0.002177778      
0.16   -0.026666667   0.000711111      
0.11   -0.076666667   0.005877778      
0.16   -0.026666667   0.000711111      
              
              
Thus, Sum(x - X)^2 =    0.036466667          
              
Thus, as               
              
s^2 = Sum(x - X)^2 / (n - 1)              
              
As n =    12          
              
s^2 =    0.003315152          

Thus,      
      
s =    0.057577352   [ANSWER, STANDARD DEVIATION]

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