Assume the body temperatures of healthy adults are normally distributed with a mean of 98.20 °F and a standard deviation of 0.62 °F (based on data from the University of Maryland researchers).

Bellevue Hospital in New York City uses 100.6 °F as the lowest temperature considered to indicate a fever. What percentage of normal and healthy adults would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6 °F is appropriate?

I ran your data through my favourite and trusty

normal distribution calculator
http://davidmlane.com/hyperstat/z_table.html

and at 100.6F only about .0054% would be considered to have a fever according to the hospital's criteria.

To determine the percentage of normal and healthy adults that would be considered to have a fever according to Bellevue Hospital's cutoff of 100.6 °F, we need to calculate the proportion of individuals with body temperatures higher than 100.6 °F.

To do this, we can use the Z-score formula:
Z = (X - μ) / σ

where Z is the Z-score, X is the value we want to convert, μ is the mean, and σ is the standard deviation.

In this case, we want to calculate the Z-score for a body temperature of 100.6 °F using the given mean of 98.20 °F and standard deviation of 0.62 °F:
Z = (100.6 - 98.20) / 0.62

Calculating, we get:
Z ≈ 3.87

Next, we need to find the percentage of individuals with a Z-score greater than 3.87 in a standard normal distribution. We can use a Z-table or a statistical calculator to find this value.

Using a Z-table, we find that the area to the right of 3.87 (which represents the percentage of individuals with body temperatures higher than 100.6 °F) is approximately 0.00007. This is equivalent to 0.007% or 0.007 out of every 100 adults.

Therefore, based on the normal distribution, the percentage of normal and healthy adults with body temperatures higher than 100.6 °F is extremely low at 0.007%. This suggests that the cutoff of 100.6 °F is appropriate for identifying individuals with potential fever symptoms in a normal and healthy population.

It's worth noting that this analysis is based on the assumption that body temperatures follow a normal distribution and on the given mean and standard deviation. Different populations or situations may have different statistics, so it's always important to consider the specific context when determining appropriate cutoffs for fever classification.