Answer:
The body temperature of a male at the 83rd percentile is 98.8°F.
Explanation:
The nth percentile implies that there are n% value below this percentile value.
That is, if P (X < x) = n% then x is the nth percentile.
Let X = male body temperature.
The random variable X follows a Normal distribution with mean, μ = 98.4°F and standard deviation, σ = 0.40°F.
Let x be the 83rd percentile value.
Then, P (X < x) = 0.83.
The value of x can be computed from the z-score.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Compute the z-score related to this probability as follows:
P (Z < z) = 0.83
*Use the z-table for the z-score.
The value of z is 0.95.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\0.96=\frac{x-98.4}{0.40} \\x=98.4+(0.96\times0.40)\\=98.784\\\approx98.8[/tex]
Thus, the body temperature of a male at the 83rd percentile is 98.8°F.
