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Most people think normal body temperature is 98.6 °F. In 1992, the Journal of the American Medical Association asserted that a more accurate figure may be 98.2 °F on average, with a standard deviation of 0.7 °F. Assuming this is true and body temperatures follow a normal distribution, 40% of the people will have a body temperature less than what value?

Options:
A) 92.693 °F
B) 95.628 °F
C) 98.025 °F
D) 100.913 °F
E) 94.205 °F

Answer :

Final answer:

To find the body temperature at which 40% of the people will have a lower body temperature, we can use the standard deviation and z-scores. The correct answer is 98.025°F.

Explanation:

To find the body temperature at which 40% of the people will have a lower body temperature, we can use the standard deviation and z-scores. Using the z-score formula, which is z = (x - mean)/standard deviation, we can find the z-score that corresponds to the 40th percentile. Then, we can use the formula z = (x - mean)/standard deviation to solve for 'x' (the body temperature in degrees Fahrenheit) given that the mean is 98.2 °F, the standard deviation is 0.7 °F, and the z-score is -0.253.

Plugging those values into the formula, we have:
-0.253 = (x - 98.2) / 0.7

Solving for 'x', we get:
x = -0.253 * 0.7 + 98.2

Therefore, the body temperature at which 40% of the people will have a lower body temperature is approximately 98.025 °F. So, the correct option is C) 98.025 °F.

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