The body temperatures of a large population of healthy adults have a distribution that is normal in shape, with a mean of 98.2 degrees Fahrenheit and a standard deviation of 0.7 degrees.

Question

06-07-2024
Mathematics

College

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The body temperatures of a large population of healthy adults have a distribution that is normal in shape, with a mean of 98.2 degrees Fahrenheit and a standard deviation of 0.7 degrees.

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vignesh67 vignesh67 · Answer 1 · 2024-02-12T00:29:42-05:00

Final answer:

The question involves the normal distribution of body temperatures in healthy adults, focusing on the mean, standard deviation, and interpretation of this data in terms of health and medical conditions.

Explanation:

The question focuses on the normal distribution of body temperatures among a large population of healthy adults. The stated distribution has a mean of 98.2 degrees Fahrenheit and a standard deviation of 0.7 degrees. Normal body temperature is typically around 37.0°C (98.6°F), with a normal range for an adult being about 36.5 to 37.5°C (97.7 to 99.5°F). Variations in body temperature can be indicators of medical conditions such as fever, infection, or circulatory problems. The provided information suggests that there are fluctuations around the setpoint, which is the physiological optimum value, yet they are considered normal as long as they stay within a certain range.

This statistical problem involves understanding how the mean and standard deviation help describe a normal distribution, and knowing how to interpret these in the context of health measurements. When the population standard deviation is unknown, and a smaller sample is taken (as in the case of the provided sample of 20 healthy adults), it is appropriate to use the t distribution for more accurate results.