PLEASE PROVIDE ALL DETAILS. A car company conducted a study to understand the re
ID: 3402926 • Letter: P
Question
PLEASE PROVIDE ALL DETAILS. A car company conducted a study to understand the relationship between age groups and drivers' primary vehicles. (Their primary vehicle is the single vehicle that they drive most often.) Selecting and contacting a random sample of 350 drivers, the company compiled the results of their data collection in the following table.
Station Wagons & Vans
Sedans
Sports & SUV’s
Other
Less than 35
17
34
22
11
36 thru 55
46
49
40
15
56 and above
32
61
16
7
1. Does is seem likely that the two events, selecting an older driver (56 and above) and selecting Station Wagon/Van driver, are independent events? PLEASE EXPLAIN IF INDEPENDENT EVENTS
2. Of the 12 sub-categories in the above table, which pairs are mutually-exclusive. Explain how you arrived at your answer.
PLEASE IDENTIFY ALL PAIRS IN NUMBER 2
Station Wagons & Vans
Sedans
Sports & SUV’s
Other
Less than 35
17
34
22
11
36 thru 55
46
49
40
15
56 and above
32
61
16
7
Explanation / Answer
a)
Probability of all drivers choosing a station wagon or van = 0.271
Probability of an older driver choosing a SW or van = 32/(61+16+32+7) = 0.276
Since the probabilities are approximately same, hence we can say that it looks like they are independent events
b)
All the pair of car types are mutually exclusive
4C2 = 6 combinations = (SW,sedan), (SW,sports), (SW,others) and remaining three pairs
Age groups are mutually exclusive 3C2 = 3 pairs
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