Question

The distribution of human body temperature in the population is assumed to be 37ºC and standard deviation of 0.85ºC. If you choose a sample of 105 people, calculate the following probabilities:

a) That the average is less than or equal to 36.9 ºC

b) That the average is greater than 38.5 ºC

c) Find what temperature is the 10% of the hottest bodies.

d) Find what temperature is the 5% of the coldest bodies.

Answer 1

Let X be the human body temperature in the population

X~ Normal ( 37, 0.85)

A sample of 105 people is choosen

Let be the sample mean of body temoerature of 105 people

~ Normal ( 37, )

a) P( <= 36.9 ) = P( < )

= P( z < -1.20)

= 1- P( z < 1.20)

= 1- 0.88493

= 0.11507

b) P( > 38.5) = P(   >   )

= P( z > 18.08)

= 1- P( z < 18.08)

= 1- 0.9999

= 0.0001

c) For the temperature that is the 10% of the hottest bodies., we need to find the 90th percentile

P( Z < z) = 0.9

P( Z < 1.282 ) =0.9

z = 1.282

   = 1.282

= 1.282

   = 37.11

d)   For the temperature that is the 5% of the coldest bodies., we need to find the 5th percentile

   P( Z < z) = 0.05

P( Z < -1.645 ) =0.05

z =-1.645

   = -1.645

= -1.645

   = 36.86