Consider the following data drawn independently from normally distributed populations: (You may find it useful to reference the appropriate table: z table or t table) X2 = 30.6 = 25.7 02? n2 = 25 012 = 98.2 = 87,4 ni = 20 a. Construct the 95% confidence interval for the difference between the population means. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) Confidence interval is to

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2. You have some coins, each of which is a penny (1 cent), a nickel (5 cents), a dime (10 cents), or a quarter (25 cents). You know that • you have twice as many pennies as nickels, • the number of dimes is one more than the number of pennies and nickels combined, you have 34 coins in total, • and the total value of your coins is $2.70 (270 cents). (a) Set up a system of linear equations for the numbers of pennies, nickels, dimes, and quarters you have. (b) Determine how many coins of each type you have, by solving the system from part (a).

3. For this question, a = 100(n1 + n4) where n1 is the first digit of your student number and n4 is the fourth digit of your student number. For Halloween, Ambrosia collected a bag of candy. Ambrosia weighed her bag and found that there were a grams of candy in total. Ambrosia ate half her candy on the first day (the day after Halloween). Her father told her that if she continued to eat it at that rate the candy would only last one more day, so Ambrosia decided that each day she would only eat half of the weight of the candy left in the bag. She hypothesised that this would allow her to eat candy every day and never run out. Ambrosia decided it might be useful to use Mathematics to think about her remaining candy. She assigns t and W such that • t is a variable representing the number of days since Halloween. • W(t) represents the weight (in grams) of the remaining candy at the end of the day t. To understand what would be an appropriate mathematical model for this problem Ambrosia…