Answer :
a) 20.33% of healthy adults have a body temperature below 98.1 degrees Fahrenheit, b) 5% of healthy adults have a body temperature above 99.2 degrees Fahrenheit.
(a) To find the percentage of healthy adults with a body temperature below 98.1 degrees, we need to calculate the z-score and then find the corresponding area under the normal curve.
The z-score formula is given by: z = (x - μ) / σ
where x is the value we want to find the percentage for, μ is the mean, and σ is the standard deviation.
For this question, x = 98.1, μ = 98.6, and σ = 0.6.
Calculating the z-score: z = (98.1 - 98.6) / 0.6 = -0.83
Now, we can look up the corresponding area under the normal curve for a z-score of -0.83 using a z-table or a calculator. The area to the left of -0.83 is approximately 0.2033 or 20.33%.
Therefore, approximately 20.33% of healthy adults have a body temperature below 98.1 degrees Fahrenheit.
(b) To find the percentage of healthy adults with a body temperature above a certain value, we can use the same z-score formula.
Let's assume we want to find the body temperature above a certain value, which we'll call "y."
The formula becomes: z = (y - μ) / σ
We want to find the value of y that corresponds to a certain percentage. In this case, we want to find the body temperature that is above 85% of healthy adults.
To do this, we need to find the z-score that corresponds to the area to the left of 85% under the normal curve. Using a z-table or a calculator, we find that the z-score is approximately 1.036.
Now, we can rearrange the z-score formula to solve for y: y = (z * σ) + μ
Substituting the values, y = (1.036 * 0.6) + 98.6 = 99.2216
Rounding to the nearest degree, approximately 85% of healthy adults have a body temperature above 99.2 degrees Fahrenheit.
To know more about body temperature, refer
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