Ashland MultiComm Services (AMS) marketing de- ent wants to increase subscriptio

Question

Ashland MultiComm Services (AMS) marketing de- ent wants to increase subscriptions for its 3-For-All ne, cable, and Internet combined service. AMS ma- has been conducting an aggressive direct-marketing aign that includes postal and electronic mailings and telephone solicitations. Feedback from these efforts indi- cates that including premium channels in this combined service is a very important factor for both current and pro- spective subscribers. After several brainstorming sessions the marketing department has decided to add premium cable channels as a no-cost benefit of subscribing to the 3-For-All service The research director, Mona Fields, is planning to con- duct a survey among prospective customers to determine how many premium channels need to be added to the 3-For- All service in order to generate a subscription to the service. Based on past campaigns and on industry-wide data, she es- timates the following: Probability of Premium ChannelsSubscriptions Number of Free 0.02 0.04 0.06 0.07 0.08 0.085 1. Ifa fa sample of 50 prospective customers is selected and no free piemium channels are included in the 3-For-All service en past results, what is the probability that than 3 customers will subscribe to the 3-For-Al service offer? All service offer? service offer? b. 0 customers rs or 1 customer will subscribe to the 3-For- 1 c. more than 4 customers w

Explanation / Answer

Solution

Let X = Number of customers in the survey who will subscribe to 3-For-All service when no free premium channels is included.

Then, X ~ B(50, p), where p = probability that no free premium channels is included = 0.02.

Back-up Theory

If X ~ B(n, p). i.e., X has Binomial Distribution with parameters n and p, where n = number of trials and p = probability of one success, then

probability mass function (pmf) of X is given by

p(x) = P(X = x) = (nCx)(px)(1 - p)n – x, x = 0, 1, 2, ……. , n ………………………………..(1)

[The above probability can also be directly obtained using Excel Function of Binomial Distribution] ……………………………………………………………………………….(1a)

Part (a)

Probability that fewer than 3 customers will subscribe to 3-For-All service when no free premium channels is included.

= P(X < 3)

= 0.921572 [using Excel Function of Binomial Distribution]ANSWER

Part (b)

Probability that 0 or 1 customer will subscribe to 3-For-All service when no free premium channels is included.

= P(X ? 1)

= 0.735771 [using Excel Function of Binomial Distribution]ANSWER

Part (c)

Probability that more than 4 customers will subscribe to 3-For-All service when no free premium channels is included.

= P(X > 4)

= 1 – 0.99679 [using Excel Function of Binomial Distribution]

= 0.00321 ANSWER

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