Final answer:
The mean body temperature of the sample is 98.4°F, with a sample standard deviation of 0.3°F and a variance of 0.09°F². You can find the value one standard deviation below the mean by subtracting the standard deviation from the mean, resulting in 98.1°F.
Step-by-step explanation:
To calculate the mean, variance, and standard deviation of body temperatures for a sample, one would follow these steps:
- Sum up all the sample temperatures to find the total.
- Divide this total by the number of temperatures in the sample to find the mean.
- To find the variance, subtract the mean from each temperature, square the result, sum up these squared differences, and then divide this sum by the number of observations minus one.
- To compute the standard deviation, take the square root of the variance.
Given the sample data provided, the mean temperature is 98.4°F, the sample standard deviation is 0.3°F. However, to calculate the variance, we would need to square the standard deviation which gives us 0.09°F² as the variance.
To find the value that is one standard deviation below the mean, we simply subtract the standard deviation from the mean: 98.4°F - 0.3°F = 98.1°F.