Analytics maths

Complete the following problems in a single excel file

Chapter 1 Problem 2

Gobblecakes is a bakery that specializes in cupcakes. The annual fixed cost to make cupcakes is $18,000. The variable cost including ingredients and labor to make a cupcake is $0.90. The bakery sells cupcakes for $3.20 apiece.

a. If the bakery sells 12,000 cupcakes annually, determine the total cost, total revenue, and profit.

b. How many cupcakes will the bakery need to sell to break even?

Chapter 1 Problem 4

Evergreen Fertilizer Company produces fertilizer. The company’s fixed monthly cost is $25,000, and its variable cost per pound of fertilizer is $0.15. Evergreen sells the fertilizer for $0.40 per pound. Determine the monthly break-even volume for the company.

Chapter 11

Problem 10

A large research hospital has accumulated statistical data on its patients for an extended period. Researchers have determined that patients who are smokers have an 18% chance of contracting a serious illness such as heart disease, cancer, or emphysema, whereas there is only a .06 probability that a nonsmoker will contract a serious illness. From hospital records, the researchers know that 23% of all hospital patients are smokers, whereas 77% are nonsmokers. For planning purposes, the hospital physician staff would like to know the probability that a given patient is a smoker if the patient has a serious illness.

Problem 12

The Senate consists of 100 senators, of whom 34 are Republicans and 66 are Democrats. A bill to increase defense appropriations is before the Senate. Thirty-five percent of the Democrats and 70% of the Republicans favor the bill. The bill needs a simple majority to pass. Using a probability tree, determine the probability that the bill will pass.

Problem 14

A metropolitan school system consists of three districts—north, south, and central. The north district contains 25% of all students, the south district contains 40%, and the central district contains 35%. A minimum-competency test was given to all students; 10% of the north district students failed, 15% of the south district students failed, and 5% of the central district students failed.

a. Develop a probability tree showing all marginal, conditional, and joint probabilities.

b. Develop a joint probability table.

c. What is the probability that a student selected at random failed the test?

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