Task 4 (of 4) Using the data from Task 3, calculate the following: Find Diagram Solution (a) Construct a two sided 95% condence interval for the population mean. Condence Interval: (b) Construct a two- sided 90% condence interval for the population mean. Condence Interval: (c) Construct an upper 95% condence interval for the population mean. Upper Condence Interval: d) Why is the upper control limit for the 90% twosided C1 the same of the upper 95% C17 e) What do you notice about the CI and the mean the company is claiming? Task 1 (of 4) Based on historical data the mean amount of ice cream dispersed from an ice cream machine at McDonalds by an experienced employee is 60z (u) with a standard deviation .3 oz (6). You randomly sample the amount of ice cream served by an experiences employee to 7 customers. Find the probabilities re and replace the image in Column 2 with your own image. ated to the sample mean for the cases listed below in Column 1 to guide your Diagram and Solution in Columns 2 and 3. Try to make your diagram as accurate as possible. You are welcome to do this on a separate piece of paper with the included area shaded Find (a) Probability the sample mean will be less than 5.9 oz. Diagram Solution (b) Probability the sample mean will be more than 6.2 oz. (c) Probability the sample mean will be between 5.7 and 6.0 Task 2 (of 4) You work for a n'niture manufacturer and lately there has been some issues with the table legs buckling, and you are not sure if there has been a change in the wood or the process that is causing a problem. Historically, the buckling strength averaged (a) 600N with a standard deviation (6 ) of 20 N. You randomly sample 6 table legs and get the following values (all measured in Newtons): [550, 575, 600, 560, 580, 540] a) What is the mean of the sampled data? Based on the sampled data, calculate the following: Find Diagram Solution Condence Interval: (b) Construct a two- sided 90% condence interval for the population mean. Condence Interval: (c) Construct a two- sided 95% condence interval for the population mean. d) Which interval is wider? e) Is the historical mean (u. = 600 N) in the interval? 0 What does this tell you about whether there has been a change in the legs and should the process be investigated further? Task 3 (of 4) Engineers at McDonalds are looking at a new ice cream machine to replace the ones that are frequently not working. The manufacture of one machine says the mean ll is 6.0 oz (u). You take a sample of 5 ice creams supplied from the machine and get the following volumes in units of oz. [6.0, 5.4, 5.7, 5.8, 5.8] a) What is the mean of the sampled data? b) What is the standard deviation of the sampled data? c) What is the probability of getting the average of the sampled volumes or less if the machine averages 6.0 02 (u)? Diagram for (c): Solution for (c): d) Based on this result do you think the machine will average 6.0 oz? Why