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Maximizing Farm Profit: Understanding Random Variables

Explore how a farmer's profit, defined as a random variable, is calculated based on prices of apples and potatoes. Learn how to determine expected profit and standard deviation, and calculate the probability of making over $100. Get ready for the upcoming quiz and exam on random variables.

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Maximizing Farm Profit: Understanding Random Variables

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  1. Are you ready for the quiz today? • Yes • No • With a little help from a friend

  2. Upcoming In Class • Sunday Homework 6 • Quiz 3 – Sept. 25th • Exam 1 – October 9th

  3. Chapter 14 Random Variables

  4. Profit as a Random Variable • A farmer has 60lbs of apples and 80lbs of potatoes to sell. • The market price of apples each day is a random variable with a mean of $0.50 and a standard deviation of $0.30. • Similarly, the mean price for potatoes is $0.30 and standard deviation is $0.20. • It costs him $5 to bring all of the apples and potatoes to the market.

  5. How would you define the random variable of Profit? • A=price of applesP=price of potatoesProfit=60A+80P-5 • A=price of applesP=price of potatoesProfit=0.5A+0.3P-5 • A=number of applesP=number of potatoesProfit=60A+80P-5 • A=number of applesP=number of potatoesProfit=0.5A+0.3P-5

  6. What is the farmer’s expected profit? • 49 • 54 • 60 • 80

  7. What is the Standard Deviation? • 23.56 • 23.98 • 24.08 • 24.19

  8. What’s the probability the farmer will make a Profit of more than $100? • -2.12 • 2.12 • 0.0228 • 0.9772

  9. Upcoming In Class • Sunday Homework 6 • Quiz 3 – Sept. 25th • Exam 1 – October 9th

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