Answer to Question #189653 in Statistics and Probability for Aditya Sharma

Question

Suppose that 3000 drivers in Wakanda were randomly breath-tested on 21 April

2019 and 116 were above the limit of 0.05 blood- alcohol level. On 15 May

2019, 4000 drivers were tested and 98 were above this level.

1.3.1 What additional information would you require before trying to draw conclusion

from these data? (5)

1.3.2 What factors, other than a real change in driver behaviours, could cause such a

drop in the proportion of above-the-limit drivers. (6)

1.4 A set of data has an interquartile range of 20 and a lower quartile of 6. If the data

is symmetrical, calculate the value of the median.

Answer 1

1.31.)

Given,

On dated 21 April 2019

116 out of 3000 drivers were tested above 0.05 blood-alcohol level

and

on dated 15 May 2019

98 out of 4000 drivers were tested above 0.05 blood-alcohol level

So, proportion of drivers that tested above 0.05 blood- alcohol level is

$p_1=\dfrac{116}{3000}=0.038\\\ \\p_2=\dfrac{98}{4000}=0.0245$

So, we can conclude that proportion of drivers that are above 0.05 blood-alcohol level is decreased on 15 May 2019.

1.3.2)

Additional information are:

a.) Self realization.

b.) Increase of awareness.

c.) Proper rules are followed by people. etc

1.3.3)

Given,

 $Q_1$ as the lower quartile, 

$Q_3$ the upper quartile and 

$Q_2$ the second quartile :

Then,

Interquartile range $= Q_3 - Q_4$

$20 = Q_3 - 6$

$Q_3 = 26$

Since the data is the data is symmetrical , So the median lies between the upper and lower quartile.

Hence, Mundu

$Q_2$ (median) = $\dfrac{(Q_3 + Q_1)}{ 2} = \dfrac{(26 + 6)}{2}\\$

$Q_2(median)= \dfrac{32}{2} = 16$

So, The median $= 16$