math research

A technology company decided to include drone manufacturing in its services. The company is currently running studies to determine which design would be best to feature this new division of the company. The company has decided each design will feature some combination of three different components to be made in-house. Once a component is manufactured it is labeled as either proficient or inefficient. The company has narrowed it down to three different designs; the Glider, the Blimp, or the Pilot. The Glider uses three parts of compo- nent A and two parts of component B, the Blimp uses two parts of components B and C, and the Pilot uses one part of each component.

A sample of 75 components, 25 of each type, will be used to make prototypes for the various designs. The sample was analyzed and 20 of component A are proficient, 25 of com- ponent B were proficient and 15 of component C are proficient. If 30 components are selected at random, what is the likelihood two prototypes of each design can be made? The Blimp is the most cost efficient design to produce. What is the likelihood that 5 prototypes can be created from a random choosing of 25 components? The Pilot showcases the company’s technology the most. What is the likelihood of creating 2 prototypes from 15 components? The Blimp has a speaker that can be added on for an additional feature; it is manufactured using one part of component A and one of component B. Assuming 50 components are se- lected at random, what is the likelihood one speaker prototype can be created once 10 Blimp prototypes have been created?

The company decides to maufacture the Blimp. Suppose there is a glitch in the machine which causes 20 out of every 100 parts of component B to be inefficient. (Assume all of component C are proficient.) Suppose also that you need to use this batch of components to build twenty Blimps to send to the flagship store to be sold, so, you randomly select the number of components needed. Construct random variable X that counts that number of inefficient components you selected. Build its cooresponding probability mass function. The store hears of the mishap and says that it already has pre-orders for ten Blimps. What is the likelihood you will be able to fill the pre-orders? The company says that the machine will not be able to be fixed anytime soon. What is the expected value of components that will be available for Blimp production at any given time? Based off of your findings, will the company be able to keep up with the demand of producing ten Blimps at a time?