Question

Suppose the horses in a large stable have a mean weight of 992lbs, and a standard deviation of 141lbs.What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 13lbs if 37 horses are sampled at random from the stable? Round your answer to four decimal places.

Answer 1

`P(\overline{x}>1123) =P(z>5.65)=0`

Explanation:

Here
`\mu=992 and \sigma=141`

We need to find
`P(\overline{x}>1123) for n=37`

As n=36>30, as per central limit theorem, distribution of
`\overline{x}` is normal with
`\mu=992 and \sigma=(\sigma)/(√(n))=(141)/(√(37))=23.18`

Now
`P(\overline{x}>1123) =P(z>(1123-992)/(23.18))`

`P(\overline{x}>1123) =P(z>5.65)=0`