Mathematical Reasoning

Probability and descriptive statistics are used all around us (think: life expectancy, batting averages, chances of rain, election results, sales, and lottery tickets). Both give us an opportunity to analyze data and are especially useful for making decisions. Each of the following problems will assess your ability to use basic probability and descriptive statistics to solve real-world quantitative problems. 1. Read the scenario and use your knowledge of probability to answer the prompt in the text box below the assignment. (20 points) Scenario: You are the marketing manager at The Best Candy Shop where the top sales item is the Dream Pop bags of flavored candies. You have been getting complaints from customers that there are not enough lemon or blueberry-flavored candies, which are favorites, and too many grape and strawberry-flavored candies. Your boss wants you to create an advertisement indicating, “All bags have equally likely flavors.” (That is, the probability of getting a strawberry-flavored candy piece is the same as getting a blueberry-flavored candy piece, etc.). As the marketing manager, you want to make sure you are advertising truthful information, so you pull a sample bag of Dream Pop candy and find the following pieces: 14 grape flavors 10 strawberry flavors 8 lemon flavors 8 blueberry flavors Calculate the probability of getting each flavor in the pack (explain how you found the probability of each: grape, strawberry, lemon, and blueberry). Using those probability values, explain to your boss why his advertising suggestion (that all bags have equally likely flavors) is incorrect. 2. Read the scenario and use your knowledge of descriptive statistics to answer parts A and B in the text box below the assignment. (20 points) Scenario: Customers at IT Phone Call Center have been complaining that they are waiting too long for service. The managers at the call center have taken notice and asked you to do some investigating to determine the typical service time for their customers for morning shifts compared to evening shifts. You collect the following samples (time in minutes): Morning shifts: 7,14,15,17,17,19,20,20,20,55 Evening shifts: 2,10,11,13,21,21,29,32,33,46 Calculate the mean, median, and mode for each shift using the data above. Explain your calculations. Determine which descriptive statistic (mean, median, or mode) you would utilize to communicate the typical service time to your boss for each shift and why. In your explanation, be sure to include which shift (morning or evening) has the quicker turn-around time.