Suppose the horse in a large stable have a mean weight of 11

Suppose the horse in a large stable have a mean weight of 1127lbs, and a variance of 19,044. What is the probability that the mean weight of the sample horses would differ from the population mean by greater than 8 lbs if 38 horses are sampled at random from the stable

Solution

variance of sample = 19,044/38 =501.1579

standard deviation, sigma = sqrt(variance) = 22.3865

for variation of 8 months,

z = (x-u)/sigma = 8/22.3865 = 0.3573

P( variation of more than 8 lbs) =2*P( z>0.3573) = 2*0.141 = 0.282