Answer :
Final answer:
This question is asking about the concept of normal distribution and how it relates to analyzing a sample of high temperatures in small towns.
Explanation:
This question is asking about the concept of normal distribution. The student is given a random sample of high temperatures in small towns and is asked to analyze the data based on the assumption that the temperatures are normally distributed.
To answer this question, we can calculate measures such as the mean and standard deviation of the temperature data, and use them to understand the distribution of the temperatures and make predictions about future observations.
Here's how we do it for the given data: (98 + 98.4 + 96.5 + 97.5 + 99.8 + 96.7 + 98.3 + 96.4 + 97 + 98.9) / 10 = 97.75 So, the average temperature is 97.75 degrees Fahrenheit. 2. **Calculating the Standard Deviation:** Standard Deviation is a measure of how spread out numbers in a data set are.
Here is a step by step process to compute standard deviation: a. Find the mean. b. Subtract the mean from each number (x) and square the result. c. Find the mean of these squared differences. d. Take the square root of the result in step c.
The given temperatures: x = [98, 98.4, 96.5, 97.5, 99.8, 96.7, 98.3, 96.4, 97, 98.9] To calculate the standard deviation, you need to perform the following steps: a. The mean (average) we've calculated above is 97.75. b. Subtract this mean from each temperature (x), square the result, and sum it all up.
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