The average height of 5 buildings in the city center is equal to J = 35.5 meters. A sixth building has just been measured at 36 = 42 meters. 1. What will the average height be if this new value is included in the calculation. 2. Challenge question (will not count): What is the variance s of the six data points if the variance of the first 5 data points is s = 8.2m?. Problem #2 A supermarket employee filled packages with nuts. The following table represents the weight distribution, expressed in pounds ("b") of a sample of 50 packages. Effective pods in pounds 5.9 6.0 6.1 Number of packets 2 16 22 6.2 10 1. Calculate: (i) the average weight, (11) the standard deviation of a packet of nuts. Deduce the value of the coefficient of variation defined by, Standard deviation Cu = expressed in % Average IMPORTANT: Do not forget to mention the appropriate unit. 2. Each pound of nuts costs $4.20. Determine without using the mean and variance formulas the mean, (ii) the standard deviation and (iii) the coefficient of variation associated with the cost of a packet of nuts. 3. For ecological reasons, a tax of 20 cents on the packaging is requested from the consumer. Resume the previous question by integrating this new information.