Answer :
The probability that a randomly selected person has a temperature of more than 100.4 °F is 0.0009 or 0.09%.
The problem states that the human body temperature is normally distributed with a mean of 98.5 °F and a standard deviation of 0.61 °F. To find the probability that a randomly selected person has a temperature of more than 100.4 °F, we need to calculate the area under the normal distribution curve to the right of 100.4 °F.
First, we need to standardize the temperature using the formula:
Z = (x - μ) / σ
where Z is the standardized value, x is the given temperature, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
Z = (100.4 - 98.5) / 0.61
Z = 3.11
Next, we need to find the area under the normal distribution curve to the right of 3.11. Using a standard normal distribution table or a calculator, we find that the probability corresponding to this Z-score is approximately 0.0009.
Therefore, the probability that a randomly selected person has a temperature of more than 100.4 °F is 0.0009 or 0.09%.
In conclusion, the probability is very low that a randomly selected person has a temperature of more than 100.4 °F, considering the given mean and standard deviation.
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