A data set includes 106 body temperatures of healthy adult humans having a mean of 98.9°F and a standard deviation of 0.63°F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6°F as the mean body temperature? Click here to view a t distribution table. Click here to view page 1 of the standard normal distribution table, Click here to view page 2 of the standard normal distribution table, What is the confidence interval estimate of the population mean u? (Round to three decimal places as needed.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
- [Click here to view page 1 of the standard normal distribution table.](URL)
- [Click here to view page 2 of the standard normal distribution table.](URL)
#### Confidence Interval Calculation:
What is the confidence interval estimate of the population mean \( \mu \)?
\[ \boxed{}^\circ F < \mu < \boxed{}^\circ F \]
(Round to three decimal places as needed.)
To calculate this confidence interval, consider the sample mean (\(\overline{x}\)), the standard deviation (\(s\)), the sample size (\(n\)), and the desired level of confidence.
#### Explanation of Resources:
- **T Distribution Table:** Use this table to find the critical value for the t-distribution, which is appropriate when the sample size is less than 30 or the population standard deviation is unknown.
- **Standard Normal Distribution Table (Pages 1 & 2):** These tables provide the critical values for the z-distribution, which is used when the population standard deviation is known, and the sample size is large (n > 30).
Use these resources to find the critical values that will allow you to calculate the bounds of the confidence interval accurately.
**Note:** Depending on the method you choose (t-distribution vs normal distribution), ensure to select the correct critical value corresponding to the 99% confidence level.
Feel free to input your calculations in the provided fields and round your answer to three decimal places for precision in reporting.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86445a01-0a3f-49cc-9d22-b352e3028fb5%2F7075c2d2-697b-4fc5-886f-7d65b8c99f44%2F1knenap_processed.png&w=3840&q=75)
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