Chapter $5$: Discrete probability distributions

Managing Ashland MultiComm Services

The Ashland MultiComm Services $($AMS$)$ marketing department wants to increase

subscriptions for its $3-$For$-$All telephone, cable, and Internet combined service. AMS

marketing has been conducting an aggressive direct$-$marketing campaign that includes postal

and electronic mailings and telephone solicitations. Feedback from these efforts indicates that

including premium channels in this combined service is a very important factor for both

current and prospective 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 conduct 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 estimates the following:

Number of Free

Premium Channels

Probability

of Subscriptions

$00\mathrm{.}02$

$10\mathrm{.}04$

$20\mathrm{.}06$

$30\mathrm{.}07$

$40\mathrm{.}08$

$50\mathrm{.}085$

$1.$ If a sample of $50$ prospective customers is selected and no free premium channels are

included in the $3-$For$-$All service offer, given past results, what is the probability that

a$.$ fewer than $3$ customers will subscribe to the $3-$For$-$All service offer?

b$.0$ customers or $1$ customer will subscribe to the $3-$For$-$All service offer$$

c$.$ more than $4$ customers will subscribe to the $3-$For$-$All service offer?

d$.$ Suppose that in the actual survey of $50$ prospective customers, $4$ customers subscribe to

the $3-$For$-$All service offer. What does this tell you about the previous estimate of the

proportion of customers who would subscribe to the $3-$For$-$All service offer?

$2.$ Instead of offering no premium free channels as in Problem $1,$ suppose that two free

premium channels are included in the $3-$For$-$All service offer. Given past results, what is the

probability that

a$.$ fewer than $3$ customers will subscribe to the $3-$For$-$All service offer$$

b$.0$ customers or $1$ customer will subscribe to the $3-$For$-$All service offer$$

c$.$ more than $4$ customers will subscribe to the $3-$For$-$All service offer$$

d$.$ Compare the results of $($a$)$ through $($c$)$ to those of Problem $1.$

e$.$ Suppose that in the actual survey of $50$ prospective customers, $6$ customers subscribe to

the $3-$For$-$All service offer. What does this tell you about the previous estimate of the

proportion of customers who would subscribe to the $3-$For$-$All service offer?

$2$

f$.$ What do the results in $($e$)$ tell you about the effect of offering free premium channels on

the likelihood of obtaining subscriptions to the $3-$For$-$All service?

$3.$ Suppose that additional surveys of $50$ prospective customers were conducted in which the

number of free premium channels was varied. The results were as follows:

Number of Free

Premium Channels

Number of

Subscriptions

$15$

$36$

$46$

$57$

How many free premium channels should the research director recommend for inclusion in

the $3-$For$-$All service? Explain.