Question

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of

98.13 degrees°F

and a standard deviation of

0.53 degrees°F.

Using the empirical​ rule, find each approximate percentage below.

a.	What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the​ mean, or between 96.54 degrees°F and 99.72 degrees°​F?
b.	What is the approximate percentage of healthy adults with body temperatures between 97.07 degrees°F and 99.19 degrees°​F?

Answer 1

Solution :

Given that ,

mean = =98.13

standard deviation = = 0.53

(A)

P( - 3< X < + 2) = 99.7%

answer=99.7%

(B)

P(97.07 < x <99.19 ) = P[(97.07 - 98.13) /0.53 < (x - ) / < (99.19 - 98.13 ) /0.53 )]

= P( -2< Z < 2)

= P(Z <2)+P(Z <-2 )

using empirical rule

=95%/2 + 95%/2

=47.5%+47.5%

=95%

answer=95%