Question $2.$ Acquisition Success and Post$-$Merger Issues

The merger and acquisitions process doesn't end with the deal closure. Without having post$-$merger

integration phase well$-$planned, the deal risks of failure. Post$-$merger integration involves combining the

two businesses$-$their assets, people, resources, and technology$-$into one in a way that creates the most value

for the future of company. After the acquisition, the healthcare company $("$NORTHERN CARE"$)$ estimates

that there will be an increased focus on production expansion and customer growth targeted marketing

strategies.

Customer retention during the integration process is one the challenges and "NORTHERN CARE"

expects to engage in series of targeted marketing campaigns to boost sales post$-$acquisition.

Research indicates the following:

There is $25\%$ chance that any given marketing campaign will significantly boost sales

On average, $10\%$ of customers make purchases after seeing a campaign, and "NORTHERN CARE"

receive an average of $200$ customer inquiries per month.

a$.$ What is the probability that at least two out of the next five marketing campaigns will

significantly boost sales?$[2]$

b$.$ If a marketing campaign has successfully boosted sales, what is the probability that it was the

third campaign launched in that quarter? $[2]$

c$.$ For the customer inquiries, find the expected number of customer purchases per month and the

standard deviation.$[2]$

Merging two companies often leads to operational disruptions which may raise in IT systems,

manufacturing practices and customer dissatisfaction. To address these challenges, "NORTHERN

CARE" has a dedicated team assigned to work on these issues. The operational disruption follows

poison distribution with an average of $4$ incidents per week. Let D represent the number of

operational disruptions in a week.

a$.$ Calculate the probability that there will be at least $3$ operational disruptions in the next week. $[3]$

b$.$ If "NORTHERN CARE" team plan to monitor operation over the next two weeks, what is the

expected number of disruptions during this period?$[1]$

c$.$ What is the probability that there are exactly $4$ operational disruptions in the next two weeks?$[2]$