# Question: sylvia is a research statistician at the tac transport accidentcommission...

###### Question details

Sylvia is a research statistician at the TAC (Transport Accident

Commission). She has just received police reports for non-fatal

car accidents over the past six months in her district. She reads

through the 120 accident reports and produces the table of data

on the right, which summarises the contributing factors for the

accidents.

Table:

Contributing factor / Frequency

Speed / 58

Alcohol / 39

Mobile phone use / 61

Drugs/ 32

Poor weather / 11

Poor road conditions / 16

Tiredness / 34

Distraction / 27

Other / 10

By analysing this data and doing some further research,

Sylvia is aiming to pinpoint the main contributing factors in

non-fatal car accidents.

a: What is the number of different factors Sylvia listed as

contributing to these accidents?

b: What is the probability that a non-fatal car accident had ‘mobile phone use’ as a contributing factor

to the accident? Give your answer correct to 2 decimal places.

c: What is the total frequency of contributing factors in these accidents?

d: On average, how many factors did Sylvia find contributed to each of the accidents?

e: What is the probability that drugs, speed or alcohol are a contributing factor in a non-fatal car

accident? Give your answer correct to 2 decimal places.

Sylvia wishes to create a Venn diagram for the interrelated car accident factors of alcohol, drugs and speed.

f: In drawing a three-circle Venn diagram, how many different categories will Sylvia create?

In re-reading the police reports, Sylvia collated the following information:

• Alcohol listed as a contributing factor: 39

• Drugs only listed as a contributing factor: 4

• Speed and alcohol but not drugs listed as a contributing factor: 20

g: Only two of the above three findings can be directly placed into a Venn diagram. Which one cannot

and why?

Sylvia also finds that:

• 75 of the 120 accidents had at least one of the three factors of alcohol, drugs or speed

• 13 of the accidents had drugs and speed as contributing factors, but not alcohol.

h: Using all the relevant information Sylvia has discovered, draw a completed three-circle Venn

diagram for the interrelated car accident factors of alcohol, drugs and speed.

i: From these police reports, what is the probability that all three factors of alcohol, drugs and speed

are involved in a non-fatal car accident?