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alekssr [168]
2 years ago
5

A television campaign is conducted during the football season to promote a well-known brand X shaving cream. For each of several

weeks, a survey is made, and it is found that each week, 60% of those using brand X continue to use it and 40% switch to another brand. It is also found that of those not using brand X, 40% switch to brand X while the other 60% continue using another brand. a) Draw a transition diagram. b) Write the transition matrix. c) If 10% of the people are using brand X at the start of the advertising campaign, what percentage will be using it 1 week later?​
Business
1 answer:
ratelena [41]2 years ago
4 0

The transition diagram is given in the attached image. See the definition of a transition diagram below.

<h3>What is a transition diagram?</h3>

A specific type of flowchart used for language analysis is called a transition diagram.

The boxes of the flowchart are represented as circles and are referred to as states in the transition diagram.

<h3>What is the Transition Matrix?</h3>

The transition matrix is given as follows:

\left[\begin{array}{cc}0.6&0.4\\0.4&0.6\end{array}\right]

<h3> If 10% of the people are using brand X at the start of the advertising campaign, what percentage will be using it 1 week later?​</h3>

If 10% of the people are using Brand X, then 90% are not using brand x. thus the initial state matrix is:

S₀ = [ 0.1, 0.9]. Thus one week later, the state matrix is:

S₁ = S₀P =  [0.1, 0.9]   *   \left[\begin{array}{cc}0.6&0.4\\0.4&0.6\end{array}\right]  

c11 = 0.1 x 0.6 + 0.9 x 0.6 = 0.6

c12 = 0.1 x 0.4 + 0.9 x 0.4 = 0.4

Hence

S₁  = [0.6, 0.4]

This means that the  percentage that will be using it 1 week later is:
0.38 = 38%

Learn more about Transition Diagrams at:
brainly.com/question/13263832
#SPJ1

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