Question

Body temperatures of healthy koalas are normally distributed with a mean of 36.6°C
and a standard deviation of 1.2°C.

a. What is the probability that a health koala has a body temperature less than
36.1°C? (1pt)

b. Veterinarians at a nature preserve in Australia thought a population of koalas
might be infected with a virus, so they chose a random sample of ? = 40 koalas
and measured their body temperatures. If they got a sample mean body
temperature less than 36.1°C, do you think that this population of koalas is
healthy? Why/why not? (4pt)

spefically need answer for part b, but i think part a is a precursor to answering part b.

Answer 1

a)

Given,

= 36.6, = 1.2

We convert this to standard normal as

P(X < x) = P( Z < x - / )

Therefore,

P(X < 36.1) = P( Z < 36.1 - 36.6 / 1.2)

= P( Z < -0.4167)

= 1 - P( Z < 0.4167)

= 1 - 0.6615

= 0.3385

b)

For random sample of n = 40, the central limit theorem is

P( < x) = P( Z < x - / ( / sqrt(n) ) )

Therefore,

P( < 36.1) = P( Z < 36.1 - 36.6 / ( 1.2 / sqrt(40) ) )

= P( Z < -2.6352)

= 1 - P( Z < 2.6352)

= 1 - 0.9958

= 0.0042

This probability is below 0.05, therefore the event that mean body temperature less than

36.1^oC is unusual.

So, this population of koalas is not healthy.