According to a random sample taken at 12 A. M., body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.1998.19degrees°F and a standard deviation of 0.560.56degrees°F. Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 33 standard deviations of the mean? What are the minimum and maximum possible body temperatures that are within 33 standard deviations of the mean?

at least 99.908% of the body temperatures of healthy adults are between 116.67 °F (maximum possible temperature for 33 standard deviations) and 79.71 °F (minimum possible temperature for 33 standard deviations)

Step-by-step explanation:

from Chebyshev's theorem:

P (|X-μ| ≤ k*σ) ≥ 1 - 1/k²

where

X = random variable = body temperatures of healthy adults

μ = expected value of X (mean)

σ = standard deviation of X

k = parameter

P (|X-μ| ≤ k*σ) = probability that X is within k-standard deviations from the mean

for our case k=33, then

P (|X-μ| ≤ 33*σ) ≥ 1 - 1/33² = 0.99908 = 99.908%

therefore at least 99.908% of the body temperatures of healthy adults are between

X max = μ + 33*σ = 98.19°F + 33 * 0.56 °F = 116.67 °F (maximum possible temperature)

and

X min = μ + 33*σ = 98.19°F - 33 * 0.56 °F = 79.71 °F (minimum possible temperature)