The managers of a car dealership are trying to determine the effect on their sal
ID: 3378967 • Letter: T
Question
The managers of a car dealership are trying to determine the effect on their sales of their arch rival’s advertising campaign. They collected data on sales which show the following result:
low
medium
high
days
Rival advertises
48
16
22
86
Doesn’t advertise
56
20
32
108
Total
104
36
54
194
With reference to the above determine the following probabilities:
(i) p(next week’s sales will be high)
(ii) p(next week’s sales will be high | the competitor advertises)
(iii) p(next week’s sales will be high | the competitor does not advertise)
(iv) p(next week’s sales will be low)
(v) p(next week’s sales will be low | the competitor advertises).
(b) Do the events ‘competitor advertises’ and ‘high sales’ appear to be independent?
low
medium
high
days
Rival advertises
48
16
22
86
Doesn’t advertise
56
20
32
108
Total
104
36
54
194
Explanation / Answer
i)
P(high) = 54/194 = 0.278350515 [ANSWER]
**********
ii)
P(high|adv) = 22/54 = 0.407407407 [ANSWER]
**********
iii)
P(high|not adv) = 32/54 = 0.592592593 [ANSWER]
************
iv)
P(low) = 104/194 = 0.536082474 [ANSWER]
**********
v)
P(low|adv) = 48/104 = 0.461538462 [ANSWER]
***********
b)
As
P(high) =/= P(high|adv) [parts i and ii]
Then THEY ARE NOT INDEPENDENT.
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