Distribution of Sample Mean Question

Question

Suppose the horses in a large stable have a mean weight of 818lbs
, and a variance of
3481
.What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 18lbs
if 34
horses are sampled at random from the stable? Round your answer to four decimal places.

Answer 1

Prob(  800 < x < 836) = Prob (  (800 - 818) / 3481/sqrt(34) < z < (836-818)/3481/sqrt(34) ) =

                             

                                    Prob (  (  -0.0301 < z < 0.0301)

 

                                    = Prob ( z < 0.0301 ) - Prob ( z < -0.0301) =

 

                                     0.5120 - 0.4880

 

                                    0.024  = 2.4%

 

With the variance that large, this result makes sense