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Answer:
The body temperature of a male at the 83rd percentile is 98.8°F.
Explanation:
The <em>n</em>th percentile implies that there are <em>n%</em> value below this percentile value.
That is, if P (<em>X </em><<em> x</em>) = n% then <em>x</em> is the <em>n</em>th percentile.
Let<em> </em><em>X</em> = male body temperature.
The random variable <em>X</em> follows a Normal distribution with mean, <em>μ</em> = 98.4°F and standard deviation, <em>σ</em> = 0.40°F.
Let <em>x</em> be the 83rd percentile value.
Then, P (X < x) = 0.83.
The value of <em>x</em> can be computed from the <em>z</em>-score.
Compute the <em>z</em>-score related to this probability as follows:
P (Z < z) = 0.83
*Use the <em>z</em>-table for the <em>z</em>-score.
The value of <em>z</em> is 0.95.
Compute the value of <em>x</em> as follows:
Thus, the body temperature of a male at the 83rd percentile is 98.8°F.