Question

Bodytemperatures ofhealthy koalasarenormally distributed with a mean of 35.6°C and a standard deviation of 1.3°C. a.What is the probability that a health koalahas a body temperature lessthan 35.0°C? (1pt)b.Veterinarians at a nature preserve in Australiathought a population of koalas might be infected with a virus, so they chose a random sample of n=30koalas and measured their body temperatures. If they got a sample mean body temperature less than 35.0°C, do you think that this population of koalas is healthy? Why/why not?Be specific.(4pt)c.List a potential confounding variable for this study and briefly how it might have impactedthe results. (2pt)2.

Answer 1

Answer:

a

 $P(X < 35) = 32.3 \%$

b

$P(\= X < 35) = 0.6 \%$

Here the probability of koalas mean temperature being less than 35 °C is very small hence the koalas are not healthy

c

A potential confounding variable for this study is  the population of the koalas because in the first question the population was not taken into account and the probability was  $P(X < 35) = 32.3 \%$ but when the population was taken into account (i.e  n =  30) the probability became

$P(\= X < 35) = 0.6 \%$  

Step-by-step explanation:

From the question we are told that

  The mean is  $\mu = 35.6^oC$

   The standard deviation is  $s = 1.3^oC$

   The sample size is  n = 30

Generally the  probability that a health koala has a body temperature less than 35.0°C is mathematically represented as

     $P(X < 35) = P(\frac{X - \mu }{s} < \frac{35 - 35.6}{1.3} )$

Here  $(\frac{X - \mu }{s} = Z (The \ standardized \ value \ of \ X )$

So

    $P(X < 35) = P(Z < -0.46)$

From the z-table  P(Z <  -0.46) =  0.323

So  

    $P(X < 35) = 0.323$

Converting to percentage

      $P(X < 35) = 0.323 * 100$

      $P(X < 35) = 32.3 \%$

considering question b

The sample mean is  $\= x = 35$

Generally the standard error of the mean is mathematically represented as

   $\sigma_{\= x} = \frac{s}{\sqrt{n} }$

=>  $\sigma_{\= x} = \frac{1.3}{\sqrt{30} }$

=>  $\sigma_{\= x} = 0.2373$

Generally the probability of the mean body temperature of koalas being less than 35.0°C is mathematically represented as

 $P(\= X < 35) = P(\frac{\= X - \mu }{\sigma_{\= x }} < \frac{35 -35.6}{0.2373 } )$

$P(\= X < 35) = P(Z< -2.53 )$

From the z-table  we have that

   $P(Z< -2.53 ) = 0.006$

So

 $P(\= X < 35) = 0.006 /tex] Converting to percentage [tex]P(\= X < 35) = 0.006 * 100$

      $P(\= X < 35) = 0.6 \%$

Here the probability of koalas mean temperature being less than 35 °C is very small hence the koalas are not healthy

A potential confounding variable for this study is  the population of the koalas because in the first question the population was not taken into account and the probability was  $P(X < 35) = 32.3 \%$ but when the population was taken into account (i.e  n =  30) the probability became

 $P(\= X < 35) = 0.6 \%$