Answer to Question #186370 in Statistics and Probability for Fazeeda

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

1.3.1) On 21 April 2019,

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

On 15 May 2019,

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

Proportion $p_1 = \dfrac{116}{3000} = 0.038$

Proportion $p_1 = \dfrac{98}{4000} = 0.0245$

We can clearly see that proportion of people had decreased on 15 may 2019.

1.3.2) Factors are:

a.) Self realization.

b.) Increase of awareness.

c.) Proper rules are followed by people.

1.3.3) Given $Q_1$ as the lower quartile, $Q_3$ the upper quartile and $Q_2$ the second quartile :

Interquartile range $= Q_3 - Q_4$

$20 = Q_3 - 6$

$Q_3 = 26$

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

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

$= \dfrac{32}{2} = 16$

The median $= 16$