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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.