Reword the following answer: # Problem 5 **Solution** First, let's organize the provided temperatures: - 45.2 - 60.4 - 66.8 - 73 - 75.3 - 53.2 - 41.8 - 88.3 - 76.1 - 106.8 - 24.6 (a) The **sample mean** is found by adding all these values together and dividing by the total number of samples. (b) The **sample standard deviation** is calculated by finding the square root of the average of the squared differences from the Mean. (c) The **95% confidence interval** for the mean temperature. It is calculated as x Z (/n). In this case, Z is the Z-score that corresponds to a 95% confidence interval, which is approximately 1.96. # Problem 6 **Solution** (a) The proportion that prefers Candidate A can be found by dividing the number who prefer Candidate A (165) by the total number of people sampled (300). This will give us the decimal value of the proportion. (b) The 90% confidence interval for the proportion can be calculated as p Z * [(p*(1 - p)) / N]. Here, p is the sample proportion, Z is the Z-score that corresponds to a 90% confidence interval (approximately 1.645), and N is the size of the sample. It's important to understand that these solutions are based on statistical principles and methods, particularly those involving the normal distribution and sample statistics. These are fundamental concepts in many fields, including but not limited to research, quality control, economics, and social sciences