Respuesta :
Answer:
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)
