in description .

Question

assume that human body temperatures are normally distributed with a population mean of 98.6 in standard deviation of .62°F. The city hospital uses 100.4°F as the lowest temperature considered to be a fever.

A) If one person is randomly selected, find the probability that his or her body temperature is 100.4°F or more. x = human body temperature

B) what percentage of people would not be considered to have a fever

c) if one person is randomly selected, find the probability that his or her body temperature is between 97.5°F and 98.9°F.

D) physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be if they only want 2% of people to succeed it?

E) if four people are randomly selected, find the probability that their mean body temperature is 99°F or more.

F) why can the central limit theorem be used in part (E) even though the sample size does not exceed 30?

Answer 1

A) z= (100.4-98.6)/.62

=1.8/.62= 2.903

use a z calculator or z tables P(x>100.4)= 0.001848= anout 0.18%

P(x>100.4)= .003/2=.0015=about 0.15% using the empirical rule, assuming z=3, 2.9 is about 3

about 0.2%

B) 100%-.18%=99.82%