Emma's On-the-Go, a large convenience store that makes a good deal of money from magazine sales, has three possible locations in the store for its magazine rack: in the front of the store (to attract "impulse buying" by all customers), on the left-hand side of the store (to attract teenagers who are on that side of the store looking at the candy and soda), and in the back of the store (to attract the adults searching through the alcohol cases). The manager at Emma's experiments over the course of several months by rotating the magazine rack among the three locations, choosing a sample of 49 days at each location. Each day, the manager records the amount of money brought in from the sale of magazines. Below are the sample mean daily sales (in dollars) for each of the locations, as well as the sample variances: Sample Sample Sample size Group mean variance Front 49 216.1 593.4 Left-hand side 49 208.7 443.2 Right-hand side 49 216.9 355.8 Send data to calculator Send data to Excel Assume that the populations of daily sales from which the above samples were drawn are approximately normally distributed and that each has the same mean and the same variance. Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place. (a) Give an estimate of this common population variance based on the variance of the sample means given. (b) Give an estimate of this common population variance by pooling the sample variances given.

Emma's On-the-Go, a large convenience store that makes a good deal of money from magazine sales, has three possible locations in the store for its magazine rack: in the front of the store (to attract "impulse buying" by all customers), on the left-hand side of the store (to attract teenagers who are on that side of the store looking at the candy and soda), and in the back of the store (to attract the adults searching through the alcohol cases). The manager at Emma's experiments over the course of several months by rotating the magazine rack among the three locations, choosing a sample of 41 days at each location. Each day, the manager records the amount of money brought in from the sale of magazines. Below are the sample mean daily sales (in dollars) for each of the locations, as well as the sample variances: Sample Sample Sample size Group mean variance Front 41 218.0 365.0 Left-hand side 41 211.1 602.5 Right-hand side 41 211.1 415.3 Send data to calculator Send data to Excel Suppose…

Although still a sophomore at college, John O'Hagan's son Billy-Sean has already created several commercial video games and is currently working on his most ambitious project to date: a game called K that purports to be a "simulation of the world." John O'Hagan has decided to set aside some office space for Billy-Sean against the northern wall in the headquarters penthouse. The construction of the partition will cost $8 per foot for the south wall and $12 per foot for the east and west walls. What are the dimensions of the office space with the largest area that can be provided for Billy-Sean with a budget of $384? What is the south wall length ft? What is the east and west wall length ft? What is its area in ft2?

Bus #7 left River Street School partially filled with students and then stopped to pick up 15 more students at the Park School. it continued on its route as follows: At the next 4 stops it dropped off two students at each stop. Three students got off at the following stop. The next six stops let off one student at each stop. Ten students then got off at the Centerville after-school-program, where five kindergarten students boarded the bus. The bus then dropped off seven kids at its last stop, leaving only the driver aboard. How many students were on the bus when it left the River Street School? Show your work and explain your reasoning.