Question

According to a random sample taken at 12​ A.M., body temperatures of healthy adults have a​ bell-shaped distribution with a mean of 98.11degreesF and a standard deviation of 0.63degreesF. Using​ Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 3 standard deviations of the​ mean? What are the minimum and maximum possible body temperatures that are within 3 standard deviations of the​ mean?

Answer 1

Answer

(A) We know that for Chebyshev's theorem, percent of values within k standard deviation is given as

percent = (1 - 1/k^2)*100

for 3 standard deviation,we have k = 3

so, required percentage of data is given as

percent = (1 - 1 /3^2)*100

= (1 - 1/9)*100

= 88.89% or 89%

(B) Given that

mean = 98.11

standard deviation = 0.63

so, minimum = mean - 3*sd

= 98.11 - 3*0.63

= 96.22

and

maximum = mean +3*sd

= 98.11 + 3*0.63

= 100.00